[ 2021 ] [ 2020 ] [ 2019 ] [ 2018 ] [ Before 2018 ] [ Edited Books/Journal Issues ]

#### Causal Expectation-Maximisation

##### Zaffalon, Marco and Antonucci, Alessandro and Cabañas, Rafael (2021).

In

*WHY-21 Workshop (@ NeurIPS 2021)*. Virtual Event , Dec 13, 2021.## BIB

@inproceedings{zaffalon2021a, author = {Zaffalon, Marco and Antonucci, Alessandro and Cabañas, Rafael}, booktitle = {{WHY}-21 Workshop (@ NeurIPS 2021)}, title = {Causal Expectation-Maximisation}, year = {2021}, address = {Virtual Event}, month = dec, eprint = {https://arxiv.org/abs/2011.02912}, eventdate = {Dec 13, 2021}, url = {https://why21.causalai.net} }

## ABS

Structural causal models are the basic modelling unit in Pearl’s causal theory; in principle they allow us to solve counterfactuals, which are at the top rung of the ladder of causation. But they often contain latent variables that limit their application to special settings. This appears to be a consequence of the fact, proven in this paper, that causal inference is NP-hard even in models characterised by polytree-shaped graphs. To deal with such a hardness, we introduce the causal EM algorithm. Its primary aim is to reconstruct the uncertainty about the latent variables from data about categorical manifest variables. Counterfactual inference is then addressed via standard algorithms for Bayesian networks. The result is a general method to approximately compute counterfactuals, be they identifiable or not (in which case we deliver bounds). We show empirically, as well as by deriving credible intervals, that the approximation we provide becomes accurate in a fair number of EM runs. These results lead us finally to argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.

#### Structural Learning of Probabilistic Sentential Decision Diagrams under Partial Closed-World Assumption

##### Antonucci, Alessandro and Facchini, Alessandro and Mattei, Lilith (2021).

In

*The Fourth Tractable Probabilistic Modelling Workshop (@ UAI 2021)*. Virtual Event , Jul 30, 2021.## BIB

@inproceedings{antonucci2021b, author = {Antonucci, Alessandro and Facchini, Alessandro and Mattei, Lilith}, booktitle = {The Fourth Tractable Probabilistic Modelling Workshop (@ UAI 2021)}, title = {Structural Learning of Probabilistic Sentential Decision Diagrams under Partial Closed-World Assumption}, year = {2021}, address = {Virtual Event}, eprint = {https://arxiv.org/abs/2107.12130}, eventdate = {Jul 30, 2021}, url = {https://sites.google.com/view/tpm2021} }

## ABS

Probabilistic sentential decision diagrams are a class of structured-decomposable probabilistic circuits especially designed to embed logical constraints. To adapt the classical LearnSPN scheme to learn the structure of these models, we propose a new scheme based on a partial closed-world assumption: data implicitly provide the logical base of the circuit. Sum nodes are thus learned by recursively clustering batches in the initial data base, while the partitioning of the variables obeys a given input vtree. Preliminary experiments show that the proposed approach might properly fit training data, and generalize well to test data, provided that these remain consistent with the underlying logical base, that is a relaxation of the training data base.

#### ADAPQUEST: A Software for Web-Based Adaptive Questionnaires based on Bayesian Networks

##### Bonesana, Claudio and Mangili, Francesca and Antonucci, Alessandro (2021).

In

*AI4EDU: Artificial Intelligence For Education (@ IJCAI2021)*. Virtual Event , Aug 20, 2021.## BIB

@inproceedings{bonesana2021a, author = {Bonesana, Claudio and Mangili, Francesca and Antonucci, Alessandro}, booktitle = {AI4EDU: Artificial Intelligence For Education (@ IJCAI2021)}, title = {ADAPQUEST: A Software for Web-Based Adaptive Questionnaires based on Bayesian Networks}, year = {2021}, address = {Virtual Event}, note = {IJCAI2021 Workshop}, eprint = {https://arxiv.org/abs/2112.14476}, eventdate = {Aug 20, 2021}, url = {http://ai4ed.cc/workshops/ijcai2021} }

## ABS

We introduce ADAPQUEST, a software tool writ- ten in Java for the development of adaptive ques- tionnaires based on Bayesian networks. Adaptiveness is intended here as the dynamical choice of the question sequence on the basis of an evolving model of the skill level of the test taker. Bayesian networks offer a flexible and highly interpretable framework to describe such testing process, especially when coping with multiple skills. ADAPQUEST embeds dedicated elicitation strategies to simplify the elicitation of the questionnaire parameters. An application of this tool for the diag- nosis of mental disorders is also discussed together with some implementation details.

#### CREPO: An Open Repository to Benchmark Credal Network Algorithms

##### Cabañas, Rafael and Antonucci, Alessandro (2021).

In De Bock, J. and Cano, A. and Miranda, E. and Moral, S. (Eds),

*International Symposium on Imprecise Probabilities: Theories and Applications (ISIPTA-2021)*. Grenada (Spain) , Jul 6-9, 2021. 147 , JMLR.org , 352–356 .## BIB

@inproceedings{cabanas2021a, author = {Cabañas, Rafael and Antonucci, Alessandro}, booktitle = {International Symposium on Imprecise Probabilities: Theories and Applications ({ISIPTA}-2021)}, title = {{CREPO}: An Open Repository to Benchmark Credal Network Algorithms}, year = {2021}, address = {Grenada (Spain)}, editor = {De Bock, J. and Cano, A. and Miranda, E. and Moral, S.}, pages = {352--356}, publisher = {JMLR.org}, volume = {147}, eprint = {http://proceedings.mlr.press/v147/cabanas21a/cabanas21a.pdf}, eventdate = {Jul 6-9, 2021}, url = {https://github.com/idsia/crepo} }

## ABS

Credal networks are a popular class of imprecise prob- abilistic graphical models obtained as a Bayesian net- work generalization based on, so-called credal, sets of probability mass functions. A Java library called CREMA has been recently released to model, process and query credal networks. Despite the NP-hardness of the (exact) task, a number of algorithms is available to approximate credal network inferences. In this paper we present CREPO, an open repository of synthetic credal networks, provided together with the exact re- sults of inference tasks on these models. A Python tool is also delivered to load these data and interact with CREMA, thus making extremely easy to evaluate and compare existing and novel inference algorithms. To demonstrate such benchmarking scheme, we propose an approximate heuristic to be used inside variable elimination schemes to keep a bound on the maximum number of vertices generated during the combination step. A CREPO-based validation against approximate procedures based on linearization and exact techniques performed in CREMA is finally discussed.

#### A New score for Adaptive Tests in Bayesian and Credal Networks

##### Antonucci, Alessandro and Mangili, Francesca and Bonesana, Claudio and Adorni, Giorgia (2021).

In Vejnarová, J. and Wilson, N. (Eds),

*Symbolic and Quantitative Approaches to Reasoning With Uncertainty*. Cham . Springer International Publishing , 399–412 .## BIB

@inproceedings{antonucci2021a, author = {Antonucci, Alessandro and Mangili, Francesca and Bonesana, Claudio and Adorni, Giorgia}, booktitle = {Symbolic and Quantitative Approaches to Reasoning With Uncertainty}, title = {A New score for Adaptive Tests in {B}ayesian and Credal Networks}, year = {2021}, address = {Cham}, editor = {Vejnarov\'a, J. and Wilson, N.}, pages = {399--412}, publisher = {Springer International Publishing}, doi = {https://doi.org/10.1007/978-3-030-86772-0_29} }

## ABS

A test is adaptive when the sequence and number of ques- tions is dynamically tuned on the basis of the estimated skills of the taker. Graphical models, such as Bayesian networks, are used for adaptive tests as they allow to model the uncertainty about the questions and the skills in an explainable fashion, especially when coping with multiple skills. A better elicitation of the uncertainty in the question/skills relations can be achieved by interval probabilities. This turns the model into a credal net- work, thus increasing the inferential complexity of the queries required to select questions. This is especially the case for the information-theoretic quantities used as scores to drive the adaptive mechanism. We present an alternative family of scores, based on the mode of the posterior proba- bilities, and hence easier to explain. This makes considerably simpler the evaluation in the credal case, without significantly affecting the quality of the adaptive process. Numerical tests on synthetic and real-world data are used to support this claim.

#### Relation Clustering in Narrative Knowledge Graphs

##### Mellace, Simone and Kanjirangat, Vani and Antonucci, Alessandro (2021).

In

*AI4Narratives Workshop (@ IJCAI-PRICAI 20)*. Virtual Event , January 7 and 8, 2021.## BIB

@inproceedings{mellace2021a, author = {Mellace, Simone and Kanjirangat, Vani and Antonucci, Alessandro}, booktitle = {{AI4Narratives} Workshop (@ {IJCAI}-{PRICAI} 20)}, title = {Relation Clustering in Narrative Knowledge Graphs}, year = {2021}, address = {Virtual Event}, eventdate = {January 7 and 8, 2021}, url = {http://ceur-ws.org/Vol-2794/paper5.pdf} }

## ABS

When coping with literary texts such as novels or short stories, the extraction of structured informa- tion in the form of a knowledge graph might be hindered by the huge number of possible relations between the entities corresponding to the characters in the novel and the consequent hurdles in gathering supervised information about them. Such issue is addressed here as an unsupervised task empow- ered by transformers: relational sentences in the original text are embedded (with SBERT) and clustered in order to merge together semantically simi- lar relations. All the sentences in the same cluster are finally summarized (with BART) and a descriptive label extracted from the summary. Preliminary tests show that such clustering might successfully detect similar relations, and provide a valuable pre- processing for semi-supervised approaches.

#### Robust Model Checking with Imprecise Markov Reward Models

##### Termine, Alberto and Antonucci, Alessandro and Facchini, Alessandro and Primiero, Giuseppe (2021).

In De Bock, J. and Cano, A. and Miranda, E. and Moral, S. (Eds),

*Proceedings of the Twelfth International Symposium on Imprecise Probabilities: Theories and Applications (ISIPTA ’21)*. Granada , Jul 6-9, 2021. Proceedings of Machine Learning Research 147 , PMLR , 299–309 .## BIB

@inproceedings{termine2021a, author = {Termine, Alberto and Antonucci, Alessandro and Facchini, Alessandro and Primiero, Giuseppe}, booktitle = {Proceedings of the Twelfth International Symposium on Imprecise Probabilities: Theories and Applications (ISIPTA '21)}, title = {Robust Model Checking with Imprecise Markov Reward Models}, year = {2021}, address = {Granada}, editor = {De Bock, J. and Cano, A. and Miranda, E. and Moral, S.}, pages = {299--309}, publisher = {PMLR}, series = {Proceedings of Machine Learning Research}, volume = {147}, eventdate = {Jul 6-9, 2021} }

## ABS

In recent years probabilistic model checking has become an important area of research because of the diffusion of computational systems of stochastic nature. Despite its great success, standard probabilistic model checking suffers the limitation of requiring a sharp specification of the probabilities governing the model behaviour. The theory of imprecise probabilities offers a natural approach to overcome such limitation by a sensitivity analysis with respect to the values of these parameters. However, only extensions based on discrete-time imprecise Markov chains have been considered so far for such a robust approach to model checking. We present a further extension based on imprecise Markov reward models. In particular, we derive efficient algorithms to compute lower and upper bounds of the expected cumulative reward and probabilistic bounded rewards based on existing results for imprecise Markov chains. These ideas are tested on a real case study involving the spend-down costs of geriatric medicine departments.

#### Logic and Model Checking by imprecise Probabilistic Interpreted Systems

##### Termine, Alberto and Antonucci, Alessandro and Primiero, Giuseppe and Facchini, Alessandro (2021).

In Rosenfeld, A. and Talmon, N. (Eds),

*Multi-Agent Systems. EUMAS 2021. Lecture Notes in Computer Science*. . 12802 , Springer, Cham , 211–227 .## BIB

@inproceedings{termine2021b, author = {Termine, Alberto and Antonucci, Alessandro and Primiero, Giuseppe and Facchini, Alessandro}, booktitle = {Multi-Agent Systems. {EUMAS} 2021. Lecture Notes in Computer Science}, title = {Logic and Model Checking by imprecise Probabilistic Interpreted Systems}, year = {2021}, editor = {Rosenfeld, A. and Talmon, N.}, pages = {211--227}, publisher = {Springer, Cham}, volume = {12802}, doi = {https://doi.org/10.1007/978-3-030-82254-5_13} }

## ABS

Stochastic multi-agent systems raise the necessity to extend probabilistic model checking to the epistemic domain. Results in this direction have been achieved by epistemic extensions of Probabilistic Computation Tree Logic and related Probabilistic Interpreted Systems. The latter, however, suffer of an important limitation: they require the probabilities governing the system’s behaviour to be fully specified. A promising way to overcome this limitation is represented by imprecise probabilities. In this paper we introduce imprecise probabilistic interpreted systems and present a related logical language and model-checking procedures based on recent advances in the study of imprecise Markov processes.

#### Cautious Classification with Data Missing not at Random using Generative Random Forests

##### Llerena, Julissa V. and Mauá, Denis. D. and Antonucci, Alessandro (2021).

In Vejnarová, J. and Wilson, N. (Eds),

*Symbolic and Quantitative Approaches to Reasoning With Uncertainty*. Cham . Springer International Publishing , 284–298 .## BIB

@inproceedings{llerena2021a, author = {Llerena, Julissa V. and Mau\'a, Denis. D. and Antonucci, Alessandro}, booktitle = {Symbolic and Quantitative Approaches to Reasoning With Uncertainty}, title = {Cautious Classification with Data Missing not at Random using Generative Random Forests}, year = {2021}, address = {Cham}, editor = {Vejnarov\'a, J. and Wilson, N.}, pages = {284--298}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-030-86772-0_21} }

## ABS

Missing data present a challenge for most machine learning approaches. When a generative probabilistic model of the data is available, an effective approach is to marginalize missing values out. Probabilistic circuits are expressive generative models that allow for efficient exact inference. However, data is often missing not at random, and marginalization can lead to overconfident and wrong conclusions. In this work, we develop an efficient algorithm for assessing the robustness of classifications made by probabilistic circuits to imputations of the non- ignorable portion of missing data at prediction time. We show that our algorithm is exact when the model satisfies certain constraints, which is the case for the recent proposed Generative Random Forests, that equip Random Forest Classifiers with a full probabilistic model of the data. We also show how to extend our approach to handle non-ignorable missing data at training time.

#### SST-BERT at SemEval-2020 Task 1: Semantic Shift Tracing by Clustering in BERT-based Embedding Spaces

##### Kanjirangat, Vani and Mitrovic, Sandra and Antonucci, Alessandro and Rinaldi, Fabio (2020).

In

*Proceedings of the 14th International Workshop on Semantic Evaluation (SemEval-2020 Task 1: Unsupervised Lexical Semantic Change Detection)*. Barcelona, Spain , Dec 12-13, 2020. Association for Computational Linguistics .## BIB

@inproceedings{kanjirangat2020b, author = {Kanjirangat, Vani and Mitrovic, Sandra and Antonucci, Alessandro and Rinaldi, Fabio}, booktitle = {Proceedings of the 14th International Workshop on Semantic Evaluation (SemEval-2020 Task 1: Unsupervised Lexical Semantic Change Detection)}, title = {SST-BERT at SemEval-2020 Task 1: Semantic Shift Tracing by Clustering in BERT-based Embedding Spaces}, year = {2020}, address = {Barcelona, Spain}, eventdate = {Dec 12-13, 2020}, month = dec, publisher = {Association for Computational Linguistics} }

## ABS

Lexical semantic change detection (also known as semantic shift tracing) is a task of identifying words that have changed their meaning over time. Unsupervised semantic shift tracing, focal point of SemEval2020, is particularly challenging. Given the unsupervised setup, in this work, we propose to identify clusters among different occurrences of each target word, considering these as representatives of different word meanings. As such, disagreements in obtained clusters naturally allow to quantify the level of semantic shift per each target word in four target languages. To leverage this idea, clustering is performed on contextualized (BERT-based) embeddings of word occurrences. The obtained results show that our approach performs well both measured separately (per language) and overall, where we surpass all provided SemEval baselines.

#### Tractable Inference in Credal Sentential Decision Diagrams

##### Lilith Mattei, Lilith and Antonucci, Alessandro and Mauá, Denis Deratani and Facchini, Alessandro and Llerena, Julissa Villanueva (2020).

*International Journal of Approximate Reasoning***125**, 26–48.## BIB

@article{mattei2020a, title = {Tractable Inference in Credal Sentential Decision Diagrams}, author = {Lilith Mattei, Lilith and Antonucci, Alessandro and Mauá, Denis Deratani and Facchini, Alessandro and Llerena, Julissa Villanueva}, year = {2020}, month = oct, doi = {10.1016/j.ijar.2020.06.005}, journal = {International Journal of Approximate Reasoning}, pages = {26--48}, volume = {125} }

## ABS

Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. They allow for a compact representation of joint probability mass functions defined over sets of Boolean variables, that are also consistent with the logical constraints defined by the circuit. The probabilities in such a model are usually “learned” from a set of observations. This leads to overconfident and prior-dependent inferences when data are scarce, unreliable or conflicting. In this work, we develop the credal sentential decision diagrams, a generalisation of their probabilistic counterpart that allows for replacing the local probabilities with (so-called credal) sets of mass functions. These models induce a joint credal set over the set of Boolean variables, that sharply assigns probability zero to states inconsistent with the logical constraints. Three inference algorithms are derived for these models. These allow to compute: (i) the lower and upper probabilities of an observation for an arbitrary number of variables; (ii) the lower and upper conditional probabilities for the state of a single variable given an observation; (iii) whether or not all the probabilistic sentential decision diagrams compatible with the credal specification have the same most probable explanation of a given set of variables given an observation of the other variables. These inferences are tractable, as all the three algorithms, based on bottom-up traversal with local linear programming tasks on the disjunctive gates, can be solved in polynomial time with respect to the circuit size. The first algorithm is always exact, while the remaining two might induce a conservative (outer) approximation in the case of multiply connected circuits. A semantics for this approximation together with an auxiliary algorithm able to decide whether or not the result is exact is also provided together with a brute-force characterization of the exact inference in these cases. For a first empirical validation, we consider a simple application based on noisy seven-segment display images. The credal models are observed to properly distinguish between easy and hard-to-detect instances and outperform other generative models not able to cope with logical constraints.

#### Learning Probabilistic Sentential Decision Diagrams by Sampling

##### Geh, Renato and Mauá, Denis Deratani and Antonucci, Alessandro (2020).

In

*Proceedings of the Eight Symposium on Knowledge Discovery, Mining and Learning (KMILE)*. Porto Alegre, RS, Brasil , Oct 20, 2020. Online Event. SBC , 129–136 .## BIB

@inproceedings{geh2020a, author = {Geh, Renato and Mauá, Denis Deratani and Antonucci, Alessandro}, title = {Learning Probabilistic Sentential Decision Diagrams by Sampling}, booktitle = {Proceedings of the Eight Symposium on Knowledge Discovery, Mining and Learning (KMILE)}, location = {Online Event}, month = oct, year = {2020}, pages = {129--136}, publisher = {SBC}, eventdate = {Oct 20, 2020}, address = {Porto Alegre, RS, Brasil}, doi = {10.5753/kdmile.2020.11968}, url = {https://sol.sbc.org.br/index.php/kdmile/article/view/11968} }

## ABS

Probabilistic circuits are deep probabilistic models with neural-network-like semantics capable of accurately and efficiently answering probabilistic queries without sacrificing expressiveness. Probabilistic Sentential Decision Diagrams (PSDDs) are a subclass of probabilistic circuits able to embed logical constraints to the circuit’s structure. In doing so, they obtain extra expressiveness with empirical optimal performance. Despite achieving competitive performance compared to other state-of-the-art competitors, there have been very few attempts at learning PSDDs from a combination of both data and knowledge in the form of logical formulae. Our work investigates sampling random PSDDs consistent with domain knowledge and evaluating against state-of-the-art probabilistic models. We propose a method of sampling that retains important structural constraints on the circuit’s graph that guarantee query tractability. Finally, we show that these samples are able to achieve competitive performance even on larger domains.

#### CREDICI: A Java Library for Causal Inference by Credal Networks

##### Cabañas, Rafael and Antonucci, Alessandro and Huber, David and Zaffalon, Marco (2020).

In Jaeger, Manfred and Nielsen, Thomas Dyhre (Eds),

*Proceedings of the 10th International Conference on Probabilistic Graphical Models (PGM 2020)*. Aalborg, Denmark , Sep 23-25, 2020. Online Event. Proceedings of Machine Learning Research , PMLR .## BIB

@inproceedings{cabanas2020a, author = {Cabañas, Rafael and Antonucci, Alessandro and Huber, David and Zaffalon, Marco}, booktitle = {Proceedings of the 10th International Conference on Probabilistic Graphical Models ({PGM} 2020)}, title = {CREDICI: A Java Library for Causal Inference by Credal Networks}, year = {2020}, address = {Aalborg, Denmark}, editor = {Jaeger, Manfred and Nielsen, Thomas Dyhre}, month = sep, publisher = {PMLR}, series = {Proceedings of Machine Learning Research}, eventdate = {Sep 23-25, 2020}, location = {Online Event}, url = {https://pgm2020.cs.aau.dk} }

## ABS

We present CREDICI, a Java open-source tool for causal inference based on credal networks. Credal networks are an extension of Bayesian networks where local probability mass functions are only constrained to belong to given, so-called credal, sets. CREDICI is based on the recent work of Zaffalon et al. (2020), where an equivalence between Pearl’s structural causal models and credal networks has been derived. This allows to reduce a counterfactual query in a causal model to a standard query in a credal network, even in the case of unidentifiable causal effects. The necessary transformations and data structures are implemented in CREDICI, while inferences are eventually computed by CREMA (Huber et al., 2020), a twin library for general credal network inference. Here we discuss the main implementation challenges and possible outlooks.

#### CREMA: A Java Library for Credal Network Inference

##### Huber, David and Cabañas, Rafael and Antonucci, Alessandro and Zaffalon, Marco (2020).

In Jaeger, Manfred and Nielsen, Thomas Dyhre (Eds),

*Proceedings of the 10th International Conference on Probabilistic Graphical Models (PGM 2020)*. Aalborg, Denmark , Sep 23-25, 2020. Online Event. Proceedings of Machine Learning Research , PMLR .## BIB

@inproceedings{huber2020a, author = {Huber, David and Cabañas, Rafael and Antonucci, Alessandro and Zaffalon, Marco}, booktitle = {Proceedings of the 10th International Conference on Probabilistic Graphical Models ({PGM} 2020)}, title = {CREMA: A Java Library for Credal Network Inference}, year = {2020}, address = {Aalborg, Denmark}, editor = {Jaeger, Manfred and Nielsen, Thomas Dyhre}, month = sep, publisher = {PMLR}, series = {Proceedings of Machine Learning Research}, eventdate = {Sep 23-25, 2020}, location = {Online Event}, url = {https://pgm2020.cs.aau.dk} }

## ABS

We present CREMA (Credal Models Algorithms), a Java library for inference in credal networks. These models are analogous to Bayesian networks, but their local parameters are only con- strained to vary in, so-called credal, sets. Inference in credal networks is intended as the com- putation of the bounds of a query with respect to those local variations. For credal networks the task is harder than in Bayesian networks, being NPPP-hard in general models. Yet, scalable approximate algorithms have been shown to provide good accuracies on large or dense mod- els, while exact techniques can be designed to process small or sparse models. CREMA embeds these algorithms and also offers an API to build and query credal networks together with a spec- ification format. This makes CREMA, whose features are discussed and described by a simple example, the most advanced tool for credal network modelling and inference developed so far.

#### Structural Causal Models are (Solvable by) Credal Networks

##### Zaffalon, Marco and Antonucci, Alessandro and Cabañas, Rafael (2020).

In Jaeger, Manfred and Nielsen, Thomas Dyhre (Eds),

*Proceedings of the 10th International Conference on Probabilistic Graphical Models (PGM 2020)*. Aalborg, Denmark , Sep 23-25, 2020. Online Event. Proceedings of Machine Learning Research , PMLR .## BIB

@inproceedings{zaffalon2020a, author = {Zaffalon, Marco and Antonucci, Alessandro and Cabañas, Rafael}, booktitle = {Proceedings of the 10th International Conference on Probabilistic Graphical Models ({PGM} 2020)}, title = {Structural Causal Models are (Solvable by) Credal Networks}, year = {2020}, address = {Aalborg, Denmark}, editor = {Jaeger, Manfred and Nielsen, Thomas Dyhre}, month = sep, publisher = {PMLR}, series = {Proceedings of Machine Learning Research}, eventdate = {Sep 23-25, 2020}, location = {Online Event}, url = {https://pgm2020.cs.aau.dk} }

## ABS

A structural causal model is made of endogenous (manifest) and exogenous (latent) variables. We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables. This allows to exactly map a causal model into a credal network. Causal inferences, such as interventions and counterfactuals, can consequently be obtained by standard algorithms for the updating of credal nets. These natively return sharp values in the identifiable case, while intervals corresponding to the exact bounds are produced for unidentifiable queries. A characterization of the causal models that allow the map above to be compactly derived is given, along with a discussion about the scalability for general models. This contribution should be regarded as a systematic approach to represent structural causal models by credal networks and hence to systematically compute causal inferences. A number of demonstrative examples is presented to clarify our methodology. Extensive experiments show that approximate algorithms for credal networks can immediately be used to do causal inference in real-size problems.

#### Two Reformulation Approaches to Maximum-A-Posteriori Inference in Sum-Product Networks

##### Mauà, Denis Deratani and Ribeiro, Heitor and Katague, Gustavo and Antonucci, Alessandro (2020).

*Proceedings of the 10th International Conference on Probabilistic Graphical Models (PGM 2020)*. Aalborg, Denmark , Sep 23-25, 2020. Online Event. Proceedings of Machine Learning Research , PMLR .## BIB

@inproceedings{maua2020a, author = {Mauà, Denis Deratani and Ribeiro, Heitor and Katague, Gustavo and Antonucci, Alessandro}, booktitle = {Proceedings of the 10th International Conference on Probabilistic Graphical Models ({PGM} 2020)}, title = {Two Reformulation Approaches to Maximum-A-Posteriori Inference in Sum-Product Networks}, year = {2020}, address = {Aalborg, Denmark}, editor = {Jaeger, Manfred and Nielsen, Thomas Dyhre}, month = sep, publisher = {PMLR}, series = {Proceedings of Machine Learning Research}, eventdate = {Sep 23-25, 2020}, location = {Online Event}, url = {https://pgm2020.cs.aau.dk} }

## ABS

There exists a dichotomy between classical probabilistic graphical models, such as Bayesian net- works (BNs), and modern tractable models, such as sum-product networks (SPNs). The former generally have intractable inference, but provide a high level of interpretability, while the latter admit a wide range of tractable inference routines, but are typically harder to interpret. Due to this dichotomy, tools to convert between BNs and SPNs are desirable. While one direction – compiling BNs into SPNs – is well discussed in Darwiche’s seminal work on arithmetic circuit compilation, the converse direction – decompiling SPNs into BNs – has received surprisingly little attention. In this paper, we fill this gap by proposing SPN2BN, an algorithm that decompiles an SPN into a BN. SPN2BN has several salient features when compared to the only other two works decompiling SPNs. Most significantly, the BNs returned by SPN2BN are minimal independence-maps that are more parsimonious with respect to the introduction of latent variables. Secondly, the output BN produced by SPN2BN can be precisely characterized with respect to a compiled BN. More specifically, a certain set of directed edges will be added to the input BN, giving what we will call the moral-closure. Lastly, it is established that our compilation-decompilation process is idempotent. This has practical significance as it limits the size of the decompiled SPN.

#### Approximate MMAP by Marginal Search

##### Antonucci, Alessandro and Tiotto, Thomas (2020).

In Brawner, Keith W. and Barták, Roman and Bell, Eric (Eds),

*Proceedings of the Thirty-Third International Florida Artificial Intelligence Research Society Conference (FLAIRS-33)*. North Miami Beach, Florida, USA , May 17-20, 2020. AAAI Press , 181-184 .## BIB

@inproceedings{antonucci2020a, author = {Antonucci, Alessandro and Tiotto, Thomas}, booktitle = {Proceedings of the Thirty-Third International Florida Artificial Intelligence Research Society Conference (FLAIRS-33)}, title = {Approximate {MMAP} by Marginal Search}, year = {2020}, address = {North Miami Beach, Florida, {USA}}, editor = {Brawner, Keith W. and Bart{\'a}k, Roman and Bell, Eric}, month = may, pages = {181-184}, publisher = {AAAI Press}, eventdate = {May 17-20, 2020} }

## ABS

We present a heuristic strategy for marginal MAP (MMAP) queries in graphical models. The algorithm is based on a reduction of the task to a polynomial number of marginal inference computations. Given an input evidence, the marginals mass functions of the variables to be explained are computed. Marginal information gain is used to decide the variables to be explained first, and their most probable marginal states are consequently moved to the evidence. The sequential iteration of this procedure leads to a MMAP explanation and the minimum information gain obtained during the process can be regarded as a confidence measure for the explanation. Preliminary experiments show that the proposed confidence measure is properly detecting instances for which the algorithm is accurate and, for sufficiently high confidence levels, the algorithm gives the exact solution or an approximation whose Hamming distance from the exact one is small.

#### Temporal Embeddings and Transformer Models for Narrative Text Understanding

##### Kanjirangat, Vani and Mellace, Simone and Antonucci, Alessandro (2020).

In Campos, Ricardo and Jorge, Alípio Mário and Jatowt, Adam and Bhatia, Sumit (Eds),

*Proceedings of Text2Story - Third Workshop on Narrative Extraction From Texts co-located with 42nd European Conference on Information Retrieval (ECIR 2020)*. Lisbon, Portugal , Apr 14, 2020. Online Event. 2593 , CEUR .## BIB

@inproceedings{kanjirangat2020a, author = {Kanjirangat, Vani and Mellace, Simone and Antonucci, Alessandro}, booktitle = {Proceedings of Text2Story - Third Workshop on Narrative Extraction From Texts co-located with 42nd European Conference on Information Retrieval (ECIR 2020)}, title = {Temporal Embeddings and Transformer Models for Narrative Text Understanding}, year = {2020}, address = {Lisbon, Portugal}, editor = {Campos, Ricardo and Jorge, Alípio Mário and Jatowt, Adam and Bhatia, Sumit}, month = apr, publisher = {CEUR}, volume = {2593}, eventdate = {Apr 14, 2020}, location = {Online Event}, url = {http://ceur-ws.org/Vol-2593/paper9.pdf} }

#### A Bayesian Approach to Conversational Recommendation Systems

##### Mangili, Francesca and Broggini, Denis and Antonucci, Alessandro and Alberti, Marco and Cimasoni, Lorenzo (2020).

In

*AAAI 2020 Workshop on Interactive and Conversational Recommendation Systems (WICRS-20)*. New York, US , Feb 8, 2020.## BIB

@inproceedings{mangili2020b, author = {Mangili, Francesca and Broggini, Denis and Antonucci, Alessandro and Alberti, Marco and Cimasoni, Lorenzo}, title = {A Bayesian Approach to Conversational Recommendation Systems}, year = {2020}, month = feb, address = {New York, US}, url = {https://sites.google.com/view/wicrs2020}, booktitle = {AAAI 2020 Workshop on Interactive and Conversational Recommendation Systems (WICRS-20)}, eventdate = {Feb 8, 2020} }

## ABS

We present a Bayesian approach to conversational recommender systems. After any interaction with the user, a probability mass function over the items is updated by the system. The conversational feature corresponds to a sequential discovery of the user preferences based on questions. Information-theoretic criteria are used to optimally shape the interactions and decide when the conversation ends. Most probable items are consequently recommended. Dedicated elicitation techniques for the prior probabilities of the parameters modelling the interactions are derived from basic structural judgements based on logical compatibility and symmetry assumptions. Such prior knowledge is combined with data for better item discrimination. Our Bayesian approach is validated against matrix factorization techniques for cold-start recommendations based on metadata using the popular benchmark data set MovieLens. Results show that the proposed approach allows to considerably reduce the number of interactions while maintaining good ranking performance.

#### Temporal Word Embeddings for Narrative Understanding

##### Claudia Volpetti, Claudia and Kanjirangat, Vani and Antonucci, Alessandro (2020).

In

*Proceedings of the Twelfth International Conference on Machine Learning and Computing (ICMLC 2020)*. Shenzhen, China , Feb 15-17, 2020. Online Event. ACM Press International Conference Proceedings Series , ACM , 68-72 .## BIB

@inproceedings{volpetti2020a, author = {Claudia Volpetti, Claudia and Kanjirangat, Vani and Antonucci, Alessandro}, booktitle = {Proceedings of the Twelfth International Conference on Machine Learning and Computing (ICMLC 2020)}, title = {Temporal Word Embeddings for Narrative Understanding}, year = {2020}, address = {Shenzhen, China}, month = feb, note = {ISBN: 978-1-4503-7642-6}, pages = {68-72}, publisher = {ACM}, series = {ACM Press International Conference Proceedings Series}, doi = {10.1145/3383972.3383988}, eventdate = {Feb 15-17, 2020}, location = {Online Event} }

## ABS

We propose temporal word embeddings as a suitable tool to study the evolution of characters and their sentiments across the plot of a narrative text. The dynamic evolution of instances within a narrative text is a challenging task, where complex behavioral evolutions and other characteristics specific to the narrative text need to be inferred and interpreted. While starting from an existing approach to the learning of these models, we propose an alternative initialization procedure which seems to be especially suited for the case of narrative text. As a validation benchmark, we use the Harry Potter series of books as a challenging case study for such character trait evolution. A benchmark data set based on temporal word analogies related to the characters in the plot of the series is considered. The results are promising, and the empirical validation seems to support the working ideas behind this proposal.

#### Conversational Recommender System by Bayesian Methods

##### Mangili, Francesca and Broggini, Denis and Antonucci, Alessandro (2020).

In Davis, Jesse and Tabia, Karim (Eds),

*Proceedings of the Fourteenth International Conference on Scalable Uncertainty Management (SUM 2020)*. Bozen-Bolzano, Italy , Sep 23-25 2020. Online Event. Lecture Notes in Artificial Intelligence 12322 , Springer, Cham , 200-213 .## BIB

@inproceedings{mangili2020a, title = {Conversational Recommender System by Bayesian Methods}, author = {Mangili, Francesca and Broggini, Denis and Antonucci, Alessandro}, year = {2020}, eventdate = {Sep 23-25 2020}, address = {Bozen-Bolzano, Italy}, booktitle = {Proceedings of the Fourteenth International Conference on Scalable Uncertainty Management (SUM 2020)}, doi = {https://doi.org/10.1007/978-3-030-58449-8_14}, editor = {Davis, Jesse and Tabia, Karim}, isbn = {978-3-030-58449-8}, pages = {200-213}, location = {Online Event}, publisher = {Springer, Cham}, series = {Lecture Notes in Artificial Intelligence}, volume = {12322} }

## ABS

We present a Bayesian approach to conversational recom- mender systems. After any interaction with the user, a probability mass function over the items is updated by the system. The conversational feature corresponds to a sequential discovery of the user preferences based on questions. Information-theoretic criteria are used to optimally shape the interactions and decide when the conversation ends. Most probable items are consequently recommended. Dedicated elicitation techniques for the prior probabilities of the parameters modelling the interactions are derived from basic structural judgements based on logical compatibility and symmetry assumptions. Such prior knowledge is combined with data for better item discrimination. Our Bayesian approach is validated against matrix factorization techniques for cold-start recommendations based on metadata using the popular benchmark data set MovieLens. Results show that the proposed approach allows to considerably reduce the number of interactions while maintaining good ranking performance.

#### Credal Sentential Decision Diagrams

##### Antonucci, Alessandro and Facchini, Alessandro and Mattei, Lilith (2019).

In De Bock, Jasper and de Campos, Cassio Polpo and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory (Eds),

*Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications (ISIPTA ’19)*. Ghent, Belgium , Jul 3-6, 2019. Proceedings of Machine Learning Research 103 , PMLR , 14–22 .## BIB

@inproceedings{antonucci2019b, author = {Antonucci, Alessandro and Facchini, Alessandro and Mattei, Lilith}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications (ISIPTA '19)}, title = {Credal Sentential Decision Diagrams}, year = {2019}, address = {Ghent, Belgium}, editor = {De Bock, Jasper and {d}e Campos, Cassio Polpo and {d}e Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, month = jul, pages = {14--22}, publisher = {PMLR}, series = {Proceedings of Machine Learning Research}, volume = {103}, bdsk-url-1 = {http://proceedings.mlr.press/v103/antonucci19a/antonucci19a.pdf}, date-modified = {2019-12-29 12:51:30 +0200}, eventdate = {Jul 3-6, 2019}, url = {http://proceedings.mlr.press/v103/antonucci19a/antonucci19a.pdf} }

## ABS

Probabilistic sentential decision diagrams are logical circuits annotated by probability mass functions on the disjunctive gates. This allows for a compact representation of joint mass functions consistent with logical constraints. We propose a*credal*generalisation of the probabilistic quantification of these models, that allows to replace the local probabilities with (credal) sets of mass functions specified by linear constraints. This induces a joint credal set, that sharply assigns probability zero to states inconsistent with the constraints. These models can support cautious estimates of the local parameters when only small amounts of training data are available. Algorithmic strategies to compute lower and upper bounds of marginal and conditional queries are provided. The task can be achieved in linear time with respect to the diagram size for marginal queries. The same can be done for conditional queries if the topology of the circuit is singly connected.

#### Exploring the Space of Probabilistic Sentential Decision Diagrams

##### Mattei, Lilith and Soares, Décio L. and Antonucci, Alessandro and Mauà, Denis Deratani and Facchini, Alessandro (2019).

In

*Proceedings of the third Tractable Probabilistic Modeling Workshop, 36th International Conference on Machine Learning, June 2019*. Long Beach, California, USA , Jun 14, 2019.## BIB

@inproceedings{mattei2019a, author = {Mattei, Lilith and Soares, D{\'e}cio L. and Antonucci, Alessandro and Mau{\`a}, Denis Deratani and Facchini, Alessandro}, booktitle = {Proceedings of the third Tractable Probabilistic Modeling Workshop, 36th International Conference on Machine Learning, June 2019}, title = {Exploring the Space of Probabilistic Sentential Decision Diagrams}, year = {2019}, address = {Long Beach, California, {USA}}, month = jun, bdsk-url-1 = {https://sites.google.com/view/icmltpm2019/home}, date-modified = {2019-12-29 12:48:35 +0200}, eventdate = {Jun 14, 2019}, url = {https://sites.google.com/view/icmltpm2019/home} }

## ABS

Probabilistic sentential decision diagrams (PSDDs) are annotated circuits providing a possibly compact specification of joint probability mass functions consistent with a formula over a set of propositional variables. PSDD inference is tractable in the sense that marginal queries can be achieved in linear time with respect to the circuit size by traversal algorithms. Unlike other probabilistic graphical models such as Bayesian networks, the problem of learning the structure for PSDDs received relatively little attention. We discuss some preliminary ideas related to the development of pure likelihood-score-based search methods for the learning of PSDD structures fitting a formula and a data set of consistent observations. A sampling algorithm for these models is also provided.

#### Reliable Discretisation of Deterministic Equations in Bayesian Networks

##### Antonucci, Alessandro (2019).

In Barták, Roman and Brawner, Keith W. (Eds),

*Proceedings of the Thirty-Second International Florida Artificial Intelligence Research Society Conference (FLAIRS-32)*. Sarasota, Florida, USA , May 19-22, 2019. AAAI Press , 453-457 .## BIB

@inproceedings{antonucci2019a, author = {Antonucci, Alessandro}, booktitle = {Proceedings of the Thirty-Second International Florida Artificial Intelligence Research Society Conference (FLAIRS-32)}, title = {Reliable Discretisation of Deterministic Equations in Bayesian Networks}, year = {2019}, address = {Sarasota, Florida, {USA}}, editor = {Bart{\'a}k, Roman and Brawner, Keith W.}, pages = {453-457}, publisher = {AAAI Press}, date-modified = {2019-12-29 19:16:31 +0200}, eventdate = {May 19-22, 2019} }

## ABS

We focus on the problem of modeling deterministic equations over continuous variables in discrete Bayesian networks. This is typically achieved by a discretisation of both input and output variables and a degenerate quantification of the corresponding conditional probability tables. This approach, based on classical probabilities, cannot properly model the information loss induced by the discretisation. We show that a reliable modeling of such epistemic uncertainty can be instead achieved by credal sets, i.e., convex sets of probability mass functions. This transforms the original Bayesian network in a credal network, possibly returning interval-valued inferences, that are robust with respect to the information loss induced by the discretisation. Algorithmic strategies for an optimal choice of the discretisation bins are also discussed.

#### NOVEL2GRAPH: Visual Summaries of Narrative Text Enhanced by Machine Learning

##### K, Vani and Antonucci, Alessandro (2019).

In Alípio, Mário Jorge and Ricardo, Campos and Adam, Jatowt and Sumit, Bhatia (Eds),

*Proceedings of Text2Story - Second Workshop on Narrative Extraction From Texts co-located with 41th European Conference on Information Retrieval (ECIR 2019)*. Cologne, Germany , Apr 14, 2019. CEUR Workshop Proceedings , 29–37 .## BIB

@inproceedings{k2019a, author = {K, Vani and Antonucci, Alessandro}, booktitle = {Proceedings of Text2Story - Second Workshop on Narrative Extraction From Texts co-located with 41th European Conference on Information Retrieval (ECIR 2019)}, date-modified = {2019-12-29 12:17:55 +0200}, eventdate = {Apr 14, 2019}, editor = {Alípio, Mário Jorge and Ricardo, Campos and Adam, Jatowt and Sumit, Bhatia}, pages = {29--37}, title = {NOVEL2GRAPH: Visual Summaries of Narrative Text Enhanced by Machine Learning}, publisher = {CEUR Workshop Proceedings}, address = {Cologne, Germany}, year = {2019} }

## ABS

A machine learning approach to the creation of visual summaries for narrative text is presented. Standard natural language processing tools for named entities recognition are used together with a clustering algorithm to detect the characters of the novel and their aliases. The most relevant ones and their relations are evaluated on the basis of a simple statistical analysis. These characters are visually depicted as nodes of an undirected graph whose edges describe relations with other characters. Specialized sentiment analysis techniques based on sentence embedding decide the colours of characters/nodes and their relations/edges. Additional information about the characters (e.g., gender) and their relations (e.g., siblings or partnerships) are returned by binary classifiers and visually depicted in the graph. For those specialized tasks, small amounts of manually annotated data are sufficient to achieve good accuracy. Compared to analogous tools, the machine learning approach we present allows for a richer representation of texts of this kind. A case study to demonstrate this approach for a series of books is also reported.

#### Modeling Deterministic Equations in Discrete Bayesian Networks by Credal Networks

##### Antonucci, Alessandro (2018).

*J. Phys.: Conf. Ser.***1065**, .## BIB

@article{antonucci2018a, author = {Antonucci, Alessandro}, date-modified = {2019-12-29 21:23:31 +0200}, issue = {212014}, journal = {J. Phys.: Conf. Ser.}, title = {Modeling Deterministic Equations in Discrete {B}ayesian Networks by Credal Networks}, volume = {1065}, year = {2018} }

#### A Credal Extension of Independent Choice Logic

##### Antonucci, Alessandro and Facchini, Alessandro (2018).

In Ciucci, Davide and Pasi, Gabriella and Vantaggi, Barbara (Eds),

*Scalable Uncertainty Management (SUM 2018): Proceedings of the Twelfth International Conference on Scalable Uncertainty Management)*. Milan, Italy , Oct 3-5, 2018. Lecture Notes in Artificial Intelligence 11142 , Springer, Cham , 35–49 .## BIB

@inproceedings{antonucci2018b, author = {Antonucci, Alessandro and Facchini, Alessandro}, booktitle = {Scalable Uncertainty Management (SUM 2018): Proceedings of the Twelfth International Conference on Scalable Uncertainty Management)}, title = {A Credal Extension of Independent Choice Logic}, year = {2018}, editor = {Ciucci, Davide and Pasi, Gabriella and Vantaggi, Barbara}, pages = {35--49}, publisher = {Springer, Cham}, series = {Lecture Notes in Artificial Intelligence}, volume = {11142}, bdsk-url-1 = {https://doi.org/10.1007/978-3-030-00461-3_3}, doi = {https://doi.org/10.1007/978-3-030-00461-3_3}, eventdate = {Oct 3-5, 2018}, address = {Milan, Italy} }

## ABS

We propose an extension of Poole’s independent choice logic based on a relaxation of the underlying independence assumptions. A credal semantics involving multiple joint probability mass functions over the possible worlds is adopted. This represents a conservative approach to probabilistic logic programming achieved by considering all the mass functions consistent with the probabilistic facts. This allows to model tasks for which independence among some probabilistic choices cannot be assumed, and a specific dependence model cannot be assessed. Preliminary tests on an object ranking application show that, despite the loose underlying assumptions, informative inferences can be extracted.

#### Set-valued Probabilistic Sentential Decision Diagrams

##### Antonucci, Alessandro and Facchini, Alessandro (2018).

In Bellodi, Elena and Schrijvers, Tom (Eds),

*Proceedings of the 5th Workshop on Probabilistic Logic Programming co-located with the 28th International Conference on Inductive Logic Programming (ILP 2018)*. Ferrara, Italy , Sep 1, 2018. CEUR Workshop Proceedings .## BIB

@inproceedings{antonucci2018c, author = {Antonucci, Alessandro and Facchini, Alessandro}, booktitle = {Proceedings of the 5th Workshop on Probabilistic Logic Programming co-located with the 28th International Conference on Inductive Logic Programming (ILP 2018)}, title = {Set-valued Probabilistic Sentential Decision Diagrams}, year = {2018}, editor = {Bellodi, Elena and Schrijvers, Tom}, publisher = {CEUR Workshop Proceedings}, bdsk-url-1 = {http://ceur-ws.org/Vol-2219/paper1.pdf}, eventdate = {Sep 1, 2018}, url = {http://ceur-ws.org/Vol-2219/paper1.pdf}, address = {Ferrara, Italy} }

## ABS

Probabilistic sentential decision diagrams are a class of arith- metic circuits locally annotated by probability mass functions. This allows for a compact representation of joint mass functions in the presence of logical constraints. Here we propose a set-valued generalisation of the probabilistic quantification in these models, that allows to replace the sharp specification of the local probabilities with linear constraints over them. This induces a (convex) set of joint probability mass functions, all consistent with the assigned logical constraints. These models should be adopted for a cautious learning of the local parameters if only small amount of data are available. Algorithmic strategies to compute the lower and upper bounds of marginal and conditional queries with respect to these sets of joint mass functions are sketched. The task can be achieved in linear time with respect to the diagram size for marginal queries and, if the diagram is singly connected, the same can be done for conditional queries.

#### Reliable Uncertain Evidence Modeling in Bayesian Networks by Credal Networks

##### Marchetti, Sabina and Antonucci, Alessandro (2018).

In Brawner, Keith W. and Rus, Vasile (Eds),

*Proceedings of the Thirty-First International Florida Artificial Intelligence Research Society Conference (FLAIRS-31)*. Melbourne, Florida, USA , May 21-23, 2018. AAAI Press , 513–518 .## BIB

@inproceedings{marchetti2018a, author = {Marchetti, Sabina and Antonucci, Alessandro}, booktitle = {Proceedings of the Thirty-First International Florida Artificial Intelligence Research Society Conference (FLAIRS-31)}, title = {Reliable Uncertain Evidence Modeling in Bayesian Networks by Credal Networks}, year = {2018}, address = {Melbourne, Florida, {USA}}, editor = {Brawner, Keith W. and Rus, Vasile}, pages = {513--518}, publisher = {AAAI Press}, bdsk-url-1 = {https://aaai.org/ocs/index.php/FLAIRS/FLAIRS18/paper/view/17696/16792}, date-modified = {2019-12-29 19:28:59 +0200}, eventdate = {May 21-23, 2018}, url = {https://aaai.org/ocs/index.php/FLAIRS/FLAIRS18/paper/view/17696/16792} }

## ABS

A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard updating in an augmented credal network, equivalent to a set of consistent Bayesian networks. A characterization of the computational complexity for this task is derived together with an efficient exact procedure for a subclass of instances. In the case of multiple uncertain evidences over the same variable, the proposed procedure can provide a set-valued version of the geometric approach to opinion pooling.

#### Imaginary Kinematics

##### Marchetti, Sabina and Antonucci, Alessandro (2018).

In Globerson, Amir and Silva, Ricardo (Eds),

*UAI 2018: Proceedings of the Thirty-Fourth Conference on Uncertainty in Artificial Intelligence*. Monterey, California, USA , Aug 6-10, 2018. AUAI Press , 104–113 .## BIB

@inproceedings{marchetti2018b, author = {Marchetti, Sabina and Antonucci, Alessandro}, booktitle = {UAI 2018: Proceedings of the Thirty-Fourth Conference on Uncertainty in Artificial Intelligence}, title = {Imaginary Kinematics}, year = {2018}, address = {Monterey, California, {USA}}, editor = {Globerson, Amir and Silva, Ricardo}, pages = {104--113}, publisher = {AUAI Press}, bdsk-url-1 = {http://auai.org/uai2018/proceedings/papers/42.pdf}, eventdate = {Aug 6-10, 2018}, url = {http://auai.org/uai2018/proceedings/papers/42.pdf} }

## ABS

We introduce a novel class of adjustment rules for a collection of beliefs. This is an extension of Lewis’ imaging to absorb probabilistic evidence in generalized settings. Unlike standard tools for belief revision, our proposal may be used when information is inconsistent with an agent’s belief base. We show that the functionals we introduce are based on the imaginary counterpart of probability kinematics for standard belief revision, and prove that, under certain conditions, all standard postulates for belief revision are satisfied.

#### The Multilabel Naive Credal Classifier

##### Antonucci, Alessandro and Corani, Giorgio (2017).

*International Journal of Approximate Reasoning***83**, 320–336.## BIB

@article{antonucci2017a, author = {Antonucci, Alessandro and Corani, Giorgio}, date-modified = {2019-12-29 12:17:05 +0200}, doi = {10.1016/j.ijar.2016.10.006}, journal = {International Journal of Approximate Reasoning}, pages = {320--336}, publisher = {Elsevier}, title = {The Multilabel Naive Credal Classifier}, volume = {83}, year = {2017}, bdsk-url-1 = {https://doi.org/10.1016/j.ijar.2016.10.006} }

## ABS

A credal classifier for multilabel data is presented. This is obtained as an extension of Zaffalon’s naive credal classifier to the case of non-exclusive class labels. The dependence relations among the labels are shaped with a tree topology. The classifier, based on a polynomial-time algorithm to compute whether or not a class label is optimal, returns a compact description of the set of optimal sequences of labels. Extensive experiments on real multilabel data show that the classifier gives more robust predictions than its Bayesian counterpart. In practice, when multiple sequences are returned in output, the Bayesian model is more likely to be inaccurate, while the sequences returned by the credal classifier are more likely to include the correct one.

#### Evaluating Interval-valued Influence Diagrams

##### Cabañas, Rafael and Antonucci, Alessandro and Cano, Andrés and Gómez-Olmedo, Manuel (2017).

*International Journal of Approximate Reasoning***80**, 393–411.## BIB

@article{cabanas2017a, author = {Caba{\~n}as, Rafael and Antonucci, Alessandro and Cano, Andr{\'e}s and G{\'o}mez-Olmedo, Manuel}, date-modified = {2019-12-29 12:17:37 +0200}, journal = {International Journal of Approximate Reasoning}, pages = {393--411}, publisher = {Elsevier}, title = {Evaluating Interval-valued Influence Diagrams}, volume = {80}, year = {2017} }

## ABS

Influence diagrams are probabilistic graphical models used to represent and solve sequential decision problems under uncertainty. Sharp numerical values are required to quantify probabilities and utilities. This might be an issue with real models, whose parameters are typically obtained from expert judgements or partially reliable data. We consider an interval-valued quantification of the parameters to gain realism in the modeling and evaluate the sensitivity of the inferences with respect to perturbations in the sharp values of the parameters. An extension of the classical influence diagrams formalism to support such interval-valued potentials is presented. The variable elimination and arc reversal inference algorithms are generalized to cope with these models. At the price of an outer approximation, the extension keeps the same complexity as with sharp values. Numerical experiments show improved performances with respect to previous methods. As a natural application, we propose these models for practical sensitivity analysis in traditional influence diagrams. The maximum perturbation level on single or multiple parameters preserving the optimal strategy can be computed. This allows the identification of the parameters deserving a more careful elicitation.

#### Adaptive Testing by Bayesian Networks with Application to Language Assessment

##### Mangili, Francesca and Bonesana, Claudio and Antonucci, Alessandro and Zaffalon, Marco and Rubegni, Elisa and Addimando, Loredana (2016).

In Micarelli, Alessandro and Stamper, John and Panourgia, Kitty (Eds),

*ITS 2016: Intelligent Tutoring Systems: 13th International Conference*. Zagreb, Croatia , Jun 7-10 2016. Lecture Notes in Computer Science , , 471–472 .## BIB

@inproceedings{mangili2016a, author = {Mangili, Francesca and Bonesana, Claudio and Antonucci, Alessandro and Zaffalon, Marco and Rubegni, Elisa and Addimando, Loredana}, booktitle = {ITS 2016: Intelligent Tutoring Systems: 13th International Conference}, editor = {Micarelli, Alessandro and Stamper, John and Panourgia, Kitty}, eventdate = {Jun 7-10 2016}, pages = {471--472}, series = {Lecture Notes in Computer Science}, title = {Adaptive Testing by {B}ayesian Networks with Application to Language Assessment}, url = {https://www.springer.com/gp/book/9783319395821}, address = {Zagreb, Croatia}, year = {2016}, bdsk-url-1 = {http://link.springer.com/content/pdf/bbm%3A978-3-319-39583-8%2F1.pdf} }

## ABS

We present a general procedure for computerized adaptive testing based on probabilistic graphical models, and show on a real-world benchmark how this procedure can increase the internal consistency of the test and reduce the number of questions without affecting accuracy.

#### Technical Gestures Recognition by Set-valued Hidden Markov Models with Prior Knowledge

##### Soullard, Yann and Antonucci, Alessandro and Destercke, Sébastien (2016).

In Ferraro, Maria Brigida and Giordani, Paolo and Vantaggi, Barbara and Gagolewski, Marek and Gil, María Ángeles and Grzegorzewski, Przemysław and Hryniewicz, Olgierd (Eds),

*Soft Methods for Data Science (SMPS 2016: Proceedings of the Eight International Conference on Soft Methods in Probability and Statistics)*. Rome, Italy , Sep 12-14, 2016. Advances in Intelligent Systems and Computing 456 , Springer , 455–462 .## BIB

@inproceedings{soullard2016a, author = {Soullard, Yann and Antonucci, Alessandro and Destercke, Sébastien}, booktitle = {Soft Methods for Data Science (SMPS 2016: Proceedings of the Eight International Conference on {S}oft {M}ethods in {P}robability and {S}tatistics)}, date-modified = {2019-12-29 12:15:07 +0200}, doi = {10.1007/978-3-319-42972-4_56}, editor = {Ferraro, Maria Brigida and Giordani, Paolo and Vantaggi, Barbara and Gagolewski, Marek and Gil, María Ángeles and Grzegorzewski, Przemysław and Hryniewicz, Olgierd}, pages = {455--462}, publisher = {Springer}, address = {Rome, Italy}, eventdate = {Sep 12-14, 2016}, series = {Advances in Intelligent Systems and Computing}, title = {Technical Gestures Recognition by Set-valued Hidden {M}arkov Models with Prior Knowledge}, volume = {456}, year = {2016}, bdsk-url-1 = {https://doi.org/10.1007/978-3-319-42972-4_56} }

## ABS

Hidden Markov models are popular tools for gesture recognition. Once the generative processes of gestures have been identified, an observation sequence is usually classified as the gesture having the highest likelihood, thus ignoring possible prior information. In this paper, we consider two potential improvements of such methods: the inclusion of prior information, and the possibility of considering convex sets of probabilities (in the likelihoods and the prior) to infer imprecise, but more reliable, predictions when information is insufficient. We apply the proposed approach to technical gestures, typically characterized by severe class imbalance. By modelling such imbalances as a prior information, we achieve more accurate results, while the imprecise quantification is shown to produce more reliable estimates.

#### Hidden Markov models with Set-valued Parameters

##### Mauá, Denis Deratani and Antonucci, Alessandro and de Campos, Cassio Polpo (2016).

*Neurocomputing***180**, 94–107.## BIB

@article{maua2016a, author = {Mau{\'a}, Denis Deratani and Antonucci, Alessandro and de Campos, Cassio Polpo}, date-modified = {2019-12-29 12:52:13 +0200}, doi = {doi:10.1016/j.neucom.2015.08.095}, journal = {Neurocomputing}, pages = {94--107}, publisher = {Elsevier}, title = {Hidden {M}arkov models with Set-valued Parameters}, volume = {180}, year = {2016}, bdsk-url-1 = {https://doi.org/10.1016/j.neucom.2015.08.095} }

## ABS

Hidden Markov models (HMMs) are widely used probabilistic models of sequential data. As with other probabilistic models, they require the specification of local conditional probability distributions, whose assessment can be too difficult and error-prone, especially when data are scarce or costly to acquire. The imprecise HMM (iHMM) generalizes HMMs by allowing the quantification to be done by sets of, instead of single, probability distributions. iHMMs have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. In this paper, we consider iHMMs under the strong independence interpretation, for which we develop efficient infer- ence algorithms to address standard HMM usage such as the computation of likelihoods and most probable explanations, as well as performing filter- ing and predictive inference. Experiments with real data show that iHMMs produce more reliable inferences without compromising the computational efficiency.

#### Approximate Credal Network Updating by Linear Programming with Applications to Decision Making

##### Antonucci, Alessandro and de Campos, Cassio Polpo and Huber, David and Zaffalon, Marco (2015).

*International Journal of Approximate Reasoning***58**, 25–38.## BIB

@article{antonucci2015c, author = {Antonucci, Alessandro and de Campos, Cassio Polpo and Huber, David and Zaffalon, Marco}, date-modified = {2019-12-29 12:16:48 +0200}, journal = {International Journal of Approximate Reasoning}, pages = {25--38}, publisher = {Elsevier}, title = {Approximate Credal Network Updating by Linear Programming with Applications to Decision Making}, volume = {58}, year = {2015} }

## ABS

Credal nets are probabilistic graphical models which extend Bayesian nets to cope with sets of distributions. An algorithm for approximate credal network updating is presented. The problem in its general formulation is a multilinear optimization task, which can be linearized by an appropriate rule for fixing all the local models apart from those of a single variable. This simple idea can be iterated and quickly leads to accurate inferences. A transformation is also derived to reduce decision making in credal networks based on the maximality criterion to updating. The decision task is proved to have the same complexity of standard inference, being NP^PP-complete for general credal nets and NP-complete for polytrees. Similar results are derived for the E-admissibility criterion. Numerical experiments confirm a good performance of the method.

#### Imprecision in Machine Learning and AI

##### de Campos, Cassio Polpo and Antonucci, Alessandro (2015).

*The IEEE Intelligent Informatics Bulletin***16**(1) , 20–23.## BIB

@article{decampos2015a, author = {de Campos, Cassio Polpo and Antonucci, Alessandro}, journal = {The {IEEE} Intelligent Informatics Bulletin}, date-modified = {2019-12-29 12:14:06 +0200}, number = {1}, pages = {20--23}, publisher = {IEEE Computer Society}, title = {Imprecision in {M}achine {L}earning and {AI}}, url = {http://www.comp.hkbu.edu.hk/~cib/2015/Dec/iib_vol16no1.pdf}, volume = {16}, year = {2015}, bdsk-url-1 = {http://www.comp.hkbu.edu.hk/~cib/2015/Dec/iib_vol16no1.pdf} }

#### Robust Classification of Multivariate Time Series by Imprecise Hidden Markov Models

##### Antonucci, Alessandro and de Rosa, Rocco and Giusti, Alessandro and Cuzzolin, Fabio (2015).

*International Journal of Approximate Reasoning***56**(B) , 249–263.## BIB

@article{antonucci2015d, author = {Antonucci, Alessandro and de Rosa, Rocco and Giusti, Alessandro and Cuzzolin, Fabio}, journal = {International Journal of Approximate Reasoning}, number = {B}, pages = {249--263}, title = {Robust Classification of Multivariate Time Series by Imprecise Hidden {M}arkov Models}, volume = {56}, year = {2015} }

## ABS

A novel technique to classify time series with imprecise hidden Markov models is presented. The learning of these models is achieved by coupling the EM algorithm with the imprecise Dirichlet model. In the stationarity limit, each model corresponds to an imprecise mixture of Gaussian densities, this reducing the problem to the classification of static, imprecise-probabilistic, information. Two classifiers, one based on the expected value of the mixture, the other on the Bhattacharyya distance between pairs of mixtures, are developed. The computation of the bounds of these descriptors with respect to the imprecise quantification of the parameters is reduced to, respectively, linear and quadratic optimization tasks, and hence efficiently solved. Classification is performed by extending the k-nearest neighbors approach to interval-valued data. The classifiers are credal, meaning that multiple class labels can be returned in the output. Experiments on benchmark datasets for computer vision show that these methods achieve the required robustness whilst outperforming other precise and imprecise methods.

#### Variable Elimination for Interval-valued Influence Diagrams

##### Cabañas, Rafael and Antonucci, Alessandro and Cano, Andrés and Gómez-Olmedo, Manuel (2015).

In Destercke, Sébastien and Denoeux, Thierry (Eds),

*ECSQARU 2013: Proceedings of the 13th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty*. Compiègne, France , Jul 15-17, 2015. Lecture Notes in Artificial Intelligence 9161 , Springer, Cham , 541–551 .## BIB

@inproceedings{cabanas2015a, author = {Caba{\~n}as, Rafael and Antonucci, Alessandro and Cano, Andr{\'e}s and G{\'o}mez-Olmedo, Manuel}, editor = {Destercke, Sébastien and Denoeux, Thierry}, booktitle = {ECSQARU 2013: Proceedings of the 13th European Conference on Symbolic and Quantitative Approaches to Reasoning {w}ith Uncertainty}, date-modified = {2019-12-29 12:52:55 +0200}, eventdate = {Jul 15-17, 2015}, series = {Lecture Notes in Artificial Intelligence}, volume = {9161}, pages = {541--551}, doi = {https://doi.org/10.1007/978-3-319-20807-7_49}, title = {Variable Elimination for Interval-valued Influence Diagrams}, address = {Compi{\`e}gne, France}, publisher = {Springer, Cham}, year = {2015} }

## ABS

Influence diagrams are probabilistic graphical models used to represent and solve decision problems under uncertainty. Sharp numerical values are required to quantify probabilities and utilities. Yet, real models are based on data streams provided by partially reliable sensors or experts. We propose an interval-valued quantification of these parameters to gain realism in the modelling and to analyse the sensitivity of the inferences with respect to perturbations of the sharp values. An extension of the classical influence diagrams formalism to support interval-valued potentials is provided. Moreover, a variable elimination algorithm especially designed for these models is developed and evalu- ated in terms of complexity and empirical performances.

#### The Multilabel Naive Credal Classifier

##### Antonucci, Alessandro and Corani, Giorgio (2015).

In Augustin, Thomas and Doria, Serena and Miranda, Enrique and Quaeghebeur, Erik (Eds),

*ISIPTA ’15: Proceedings of the Ninth International Symposium on Imprecise Probability: Theories and Applications*. Pescara, Italy , Jul 20-24, 2015. SIPTA .## BIB

@inproceedings{antonucci2015b, author = {Antonucci, Alessandro and Corani, Giorgio}, editor = {Augustin, Thomas and Doria, Serena and Miranda, Enrique and Quaeghebeur, Erik}, booktitle = {ISIPTA '15: Proceedings of the Ninth International Symposium on Imprecise Probability: Theories and Applications}, date-modified = {2019-12-29 12:26:29 +0200}, eventdate = {Jul 20-24, 2015}, publisher = {SIPTA}, title = {The Multilabel Naive Credal Classifier}, address = {Pescara, Italy}, year = {2015} }

## ABS

We present a credal classifier for multilabel data. The model generalizes the naive credal classifier to the multilabel case. An imprecise-probabilistic quantifi- cation is achieved by means of the imprecise Dirichlet model in its global formulation. A polynomial-time algorithm to compute whether or not a label is opti- mal according to the maximality criterion is derived. Experimental results show the importance of robust predictions in multilabel problems.

#### Early Classification of Time Series by Hidden Markov Models with Set-valued Parameters

##### Antonucci, Alessandro and Scanagatta, Mauro and Mauá, Denis Deratani and de Campos, Cassio Polpo (2015).

In

*Proceedings of the NIPS Time Series Workshop 2015*. Montréal, Canada , Dec 11, 2015.## BIB

@inproceedings{antonucci2015a, author = {Antonucci, Alessandro and Scanagatta, Mauro and Mau{\'a}, Denis Deratani and de Campos, Cassio Polpo}, date-modified = {2019-12-29 12:53:26 +0200}, eventdate = {Dec 11, 2015}, booktitle = {Proceedings of the NIPS Time Series Workshop 2015}, title = {Early Classification of Time Series by Hidden {M}arkov Models with Set-valued Parameters}, url = {https://sites.google.com/site/nipsts2015/home}, address = {Montr{\'e}al, Canada}, year = {2015}, bdsk-url-1 = {https://sites.google.com/site/nipsts2015/home} }

## ABS

Hidden Markov models are popular tools for the modeling of multivariate time series. A set-valued quantification of the parameters might increase realism in the description of non-stationarity. A recent work shows that the computation of the bounds of the likelihood of a sequence with respect to such imprecise quantification can be performed in the same polynomial time of a precise computation with sharp values. This is the basis for a credal classifier of time series. For each training sequence we learn a set-valued model and compute the interval likelihood of the test sequence. The returned classes are those of the models associated to the undominated intervals. The approach is particularly accurate on the instances for which single classes are returned. We therefore apply this method to early classi- fication of streaming data. As soon as the credal classifier returns a single output we assign a class label even if the stream is not terminated. Tests on a speech recognition benchmark suggest that the proposed approach might outperform a thresholding of the precise likelihoods with the classical models.

#### Trading Off Speed and Accuracy in Multilabel Classification

##### Corani, Giorgio and Antonucci, Alessandro and Mauá, Denis Deratani and Gabaglio, Sandra (2014).

In van der Gaag, Linda C. and Feelders, Ad (Eds),

*PGM ’14: Proceedings of the Seventh European Workshop on Probabilistic Graphical Models*. Utrecht, The Netherlands , Sep 17-19, 2014. Lecture Notes in Artificial Intelligence , Springer , 145–159 .## BIB

@inproceedings{corani2014a, author = {Corani, Giorgio and Antonucci, Alessandro and Mau{\'a}, Denis Deratani and Gabaglio, Sandra}, booktitle = {PGM '14: Proceedings of the Seventh European Workshop on Probabilistic Graphical Models}, date-modified = {2019-12-29 12:54:32 +0200}, editor = {van der Gaag, Linda C. and Feelders, Ad}, eventdate = {Sep 17-19, 2014}, pages = {145--159}, publisher = {Springer}, series = {Lecture Notes in Artificial Intelligence}, title = {Trading Off Speed and Accuracy in Multilabel Classification}, address = {Utrecht, The Netherlands}, year = {2014} }

## ABS

In previous work, we devised an approach for multilabel classification based on an ensemble of Bayesian networks. It was characterized by an efficient structural learning and by high accuracy. Its shortcoming was the high computational complexity of the MAP inference, necessary to identify the most probable joint configuration of all classes. In this work, we switch from the ensemble approach to the single model approach. This allows important computational savings. The reduction of inference times is exponential in the difference between the treewidth of the single model and the number of classes. We adopt moreover a more sophisticated approach for the structural learning of the class subgraph. The proposed single models outperforms alternative approaches for multilabel classification such as binary relevance and ensemble of classifier chains.

#### Probabilistic Inference in Credal Networks: New Complexity Results

##### Mauá, Denis Deratani and de Campos, Cassio Polpo and Benavoli, Alessio and Antonucci, Alessandro (2014).

*Journal of Artificial Intelligence Research***50**, 603–637.## BIB

@article{maua2014b, author = {Mau{\'a}, Denis Deratani and de Campos, Cassio Polpo and Benavoli, Alessio and Antonucci, Alessandro}, date-modified = {2019-12-29 12:45:33 +0200}, journal = {Journal of Artificial Intelligence Research}, pages = {603--637}, title = {Probabilistic Inference in Credal Networks: New Complexity Results}, volume = {50}, year = {2014} }

## ABS

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that infer- ences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove a similar result for inference in naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and naive Bayes structures are used in real applications of imprecise probability.

#### Hidden Markov Models with Imprecisely Specified Parameters

##### Mauá, Denis Deratani and de Campos, Cassio Polpo and Antonucci, Alessandro (2014).

In

*BRACIS 2014: Proceedings of the Brazilian Conference on Intelligent Systems*. São Carlos, São Paulo, Brazil , Oct 18-23, 2014.## BIB

@inproceedings{maua2014a, author = {Mau{\'a}, Denis Deratani and de Campos, Cassio Polpo and Antonucci, Alessandro}, booktitle = {BRACIS 2014: Proceedings of the Brazilian Conference on Intelligent Systems}, date-modified = {2019-12-29 21:18:38 +0200}, eventdate = {Oct 18-23, 2014}, title = {Hidden {M}arkov Models with Imprecisely Specified Parameters}, address = {S{\~a}o Carlos, S{\~a}o Paulo, Brazil}, year = {2014} }

## ABS

Hidden Markov models (HMMs) are widely used models for sequential data. As with other probabilistic graphical models, they require the specification of precise probability values, which can be too restrictive for some domains, espe- cially when data are scarce or costly to acquire. We present a generalized version of HMMs, whose quantification can be done by sets of, instead of single, probability distributions. Our models have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. Efficient inference algorithms are developed to address standard HMM usage such as the computation of likelihoods and most probable explanations. Experiments with real data show that the use of imprecise probabilities leads to more reliable inferences without compromising efficiency.

##### De Bock, Jasper and de Campos, Cassio Polpo and Antonucci, Alessandro (2014).

In Ghahramani, Zoubin and Welling, Max and Cortes, Corinna and Lawrence, Neil D. and Weinberger, Kilian Q. (Eds),

*Advances in Neural Information Processing Systems 27 (NIPS 2014)*. Montreal, Quebec, Canada , Dec 8-13, 2014.## BIB

@inproceedings{debock2014a, author = {De Bock, Jasper and de Campos, Cassio Polpo and Antonucci, Alessandro}, booktitle = {Advances in Neural Information Processing Systems 27 (NIPS 2014)}, date-modified = {2019-12-29 12:13:14 +0200}, eventdate = {Dec 8-13, 2014}, editor = {Ghahramani, Zoubin and Welling, Max and Cortes, Corinna and Lawrence, Neil D. and Weinberger, Kilian Q.}, address = {Montreal, Quebec, Canada}, year = {2014}, url = {http://papers.nips.cc/book/advances-in-neural-information-processing-systems-27-2014}, timestamp = {Fri, 06 Mar 2020 16:57:46 +0100}, biburl = {https://dblp.org/rec/conf/nips/2014.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }

## ABS

We study the sensitivity of a MAP configuration of a discrete probabilistic graph- ical model with respect to perturbations of its parameters. These perturbations are global, in the sense that simultaneous perturbations of all the parameters (or any chosen subset of them) are allowed. Our main contribution is an exact algorithm that can check whether the MAP configuration is robust with respect to given per- turbations. Its complexity is essentially the same as that of obtaining the MAP configuration itself, so it can be promptly used with minimal effort. We use our algorithm to identify the largest global perturbation that does not induce a change in the MAP configuration, and we successfully apply this robustness measure in two practical scenarios: the prediction of facial action units with posed images and the classification of multiple real public data sets. A strong correlation between the proposed robustness measure and accuracy is verified in both scenarios.

#### Decision Making with Hierarchical Credal Sets

##### Antonucci, Alessandro and Karlsson, Alexander and Sundgren, David (2014).

In Laurent, A. and Strauss, O. and Bouchon-Meunier, B. and Yager, R.R. (Eds),

*Information Processing and Management of Uncertainty in Knowledge-Based Systems*. Montpellier, France , Jul 15-19, 2014. Communications in Computer and Information Science 444 , Springer , 456–465 .## BIB

@inproceedings{antonucci2014a, author = {Antonucci, Alessandro and Karlsson, Alexander and Sundgren, David}, booktitle = {Information Processing and Management of Uncertainty in Knowledge-Based Systems}, editor = {Laurent, A. and Strauss, O. and Bouchon-Meunier, B. and Yager, R.R.}, eventdate = {Jul 15-19, 2014}, pages = {456--465}, publisher = {Springer}, series = {Communications in Computer and Information Science}, title = {Decision Making with Hierarchical Credal Sets}, address = {Montpellier, France}, volume = {444}, year = {2014} }

#### CREDO: A Military Decision-Support System Based on Credal Networks

##### Antonucci, Alessandro and Huber, David and Zaffalon, Marco and Luginbühl, Philippe and Chapman, Ian and Ladouceur, Richard (2013).

In

*Proceedings of the 16th Conference on Information Fusion (FUSION 2013)*. Istanbul, Turkey , Jul 9-12, 2013.## BIB

@inproceedings{antonucci2013c, author = {Antonucci, Alessandro and Huber, David and Zaffalon, Marco and Luginb{\"u}hl, Philippe and Chapman, Ian and Ladouceur, Richard}, booktitle = {Proceedings of the 16th Conference on Information Fusion ({FUSION} 2013)}, date-modified = {2019-12-29 21:25:00 +0200}, eventdate = {Jul 9-12, 2013}, title = {CREDO: A Military Decision-Support System Based on Credal Networks}, address = {Istanbul, Turkey}, year = {2013} }

## ABS

A software tool especially designed for military domains to create and query decision-support systems is presented. Credal networks, which are Bayesian networks whose parameters have the freedom to vary in convex sets, are used to model the relations among the system variables. A novel elicitation procedure of these sets, which allows the military experts to report their knowledge by purely qualitative judgements, is proposed. Two high-level fusion procedures to cope with multiple experts in this framework are also derived. All these features are supported by the software and demonstrated in an application to space security tested during the last NATO multinational experiment.

#### Approximating Credal Network Inferences by Linear Programming

##### Antonucci, Alessandro and de Campos, Cassio Polpo and Huber, David and Zaffalon, Marco (2013).

In van der Gaag, Linda C. (Eds),

*Proceedings of the 12th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty*. Utrecht, The Netherlands , Jul 7-10, 2013. Lecture Notes in Artificial Intelligence 7958 , Springer , 13-25 .## BIB

@inproceedings{antonucci2013a, address = {Utrecht, The Netherlands}, author = {Antonucci, Alessandro and de Campos, Cassio Polpo and Huber, David and Zaffalon, Marco}, booktitle = {Proceedings of the 12th European Conference on Symbolic and Quantitative Approaches to Reasoning {w}ith Uncertainty}, editor = {van der Gaag, Linda C.}, eventdate = {Jul 7-10, 2013}, pages = {13-25}, publisher = {Springer}, series = {Lecture Notes in Artificial Intelligence}, title = {Approximating Credal Network Inferences by Linear Programming}, volume = {7958}, year = {2013} }

## ABS

An algorithm for approximate credal network updating is presented. The problem in its general formulation is a multilinear optimization task, which can be linearized by an appropriate rule for fixing all the local models apart from those of a single variable. This simple idea can be iterated and quickly leads to very accurate inferences. The approach can also be specialized to classification with credal networks based on the maximality criterion. A complexity analysis for both the problem and the algorithm is reported together with numerical experiments, which confirm the good performance of the method. While the inner approximation produced by the algorithm gives rise to a classifier which might return a subset of the optimal class set, preliminary empirical results suggest that the accuracy of the optimal class set is seldom affected by the approximate probabilities.

#### Temporal Data Classification by Imprecise Dynamical Models

##### Antonucci, Alessandro and de Rosa, Rocco and Giusti, Alessandro and Cuzzolin, Fabio (2013).

In Cozman, Fabio Gagliardi and Denoeux, T. and Destercke, Sébastien and Seidenfeld, Teddy (Eds),

*ISIPTA ’13: Proceedings of the Eighth International Symposium on Imprecise Probability: Theories and Applications*. Compiègne, France , Jul 2-5, 2013. SIPTA .## BIB

@inproceedings{antonucci2013b, author = {Antonucci, Alessandro and de Rosa, Rocco and Giusti, Alessandro and Cuzzolin, Fabio}, booktitle = {ISIPTA '13: Proceedings of the Eighth International Symposium on Imprecise Probability: Theories and Applications}, editor = {Cozman, Fabio Gagliardi and Denoeux, T. and Destercke, Sébastien and Seidenfeld, Teddy}, eventdate = {Jul 2-5, 2013}, publisher = {SIPTA}, title = {Temporal Data Classification by Imprecise Dynamical Models}, address = {Compi{\`e}gne, France}, year = {2013} }

## ABS

We propose a new methodology to classify temporal data with imprecise hidden Markov models. For each sequence we learn a different model by coupling the EM algorithm with the imprecise Dirichlet model. As a model descriptor, we consider the expected value of the observable variable in the limit of stationarity of the Markov chain. In the imprecise case, only the bounds of this descriptor can be evaluated. In practice the sequence, which can be regarded as a trajectory in the feature space, is summarized by a hyperbox in the same space. We classify these static but interval-valued data by a credal generalization of the k-nearest neighbors algorithm. Experiments on benchmark datasets for computer vision show that the method achieves the required robustness whilst outperforming other precise and imprecise methods.

#### An Ensemble of Bayesian Networks for Multilabel Classification

##### Antonucci, Alessandro and Corani, Giorgio and Mauá, Denis Deratani and Gabaglio, Sandra (2013).

In

*Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI-13)*. Beijing, China , Aug 3-9, 2013.## BIB

@inproceedings{antonucci2013d, author = {Antonucci, Alessandro and Corani, Giorgio and Mau{\'a}, Denis Deratani and Gabaglio, Sandra}, booktitle = {Proceedings of the 23rd International Joint Conference on Artificial Intelligence ({IJCAI}-13)}, date-modified = {2019-12-29 12:55:17 +0200}, eventdate = {Aug 3-9, 2013}, title = {An {E}nsemble of {B}ayesian {N}etworks for {M}ultilabel {C}lassification}, address = {Beijing, China}, year = {2013} }

## ABS

We present a novel approach for multilabel classification based on an ensemble of Bayesian networks. The class variables are connected by a tree; each model of the ensemble uses a different class as root of the tree. We assume the features to be conditionally independent given the classes, thus generalizing the naive Bayes assumption to the multiclass case. This assumption allows us to optimally identify the correlations between classes and features; such correlations are moreover shared across all models of the ensemble. Inferences are drawn from the ensemble via logarithmic opinion pooling. To minimize Hamming loss, we compute the marginal probability of the classes by running standard inference on each Bayesian network in the ensemble, and then pooling the inferences. To instead minimize the subset 0/1 loss, we pool the joint distributions of each model and cast the problem as a MAP inference in the corresponding graphical model. Experiments show that the approach is competitive with state-of-the-art methods for multilabel classification.

#### On the Complexity of Strong and Epistemic Credal Networks

##### Mauá, Denis Deratani and de Campos, Cassio Polpo and Benavoli, Alessio and Antonucci, Alessandro (2013).

In Nicholson, Ann and Smyth, Padhraic (Eds),

*Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence*. Bellevue, Washington , Jul 11-15, 2013. AUAI Press , 391–400 .## BIB

@inproceedings{maua2013a, author = {Mau{\'a}, Denis Deratani and de Campos, Cassio Polpo and Benavoli, Alessio and Antonucci, Alessandro}, booktitle = {Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence}, title = {On the {C}omplexity of {S}trong and {E}pistemic {C}redal {N}etworks}, year = {2013}, editor = {Nicholson, Ann and Smyth, Padhraic}, pages = {391--400}, date-modified = {2019-12-29 21:21:06 +0200}, eventdate = {Jul 11-15, 2013}, publisher = {AUAI Press}, address = {Bellevue, Washington} }

## ABS

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with ternary variables. We prove that under epistemic irrelevance the polynomial time complexity of inferences in credal trees is not likely to extend to more general models (e.g. singly connected networks). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding computational complexity.

#### Compression-based AODE Classifiers

##### Corani, Giorgio and Antonucci, Alessandro and de Rosa, Rocco (2012).

In De Raedt, L. and Bessiere, C. and Dubois, D. and Doherty, P. and Frasconi, P. and Heintz, F. and Lucas, P.J.F. (Eds),

*Proceedings 20th European Conference on Artificial Intelligence (ECAI 2012)*. Montpellier, France , Aug 27-31, 2012. Frontiers in Artificial Intelligence and Applications 242 , IOS Press , 264–269 .## BIB

@inproceedings{corani2012a, author = {Corani, Giorgio and Antonucci, Alessandro and de Rosa, Rocco}, booktitle = {Proceedings 20th European Conference on Artificial Intelligence (ECAI 2012)}, date-modified = {2019-12-29 12:17:43 +0200}, editor = {De Raedt, L. and Bessiere, C. and Dubois, D. and Doherty, P. and Frasconi, P. and Heintz, F. and Lucas, P.J.F.}, eventdate = {Aug 27-31, 2012}, pages = {264--269}, publisher = {IOS Press}, series = {Frontiers in Artificial Intelligence and Applications}, title = {Compression-based {AODE} Classifiers}, address = {Montpellier, France}, volume = {242}, year = {2012} }

## ABS

We propose the COMP-AODE classifier, which adopts the compression-based approach to average the posterior probabilities computed by different non-naive classifier (SPODEs). COMP-AODE improves classification performance over the well-known AODE model. COMP-AODE assumes a uniform prior over the SPODEs; we then develop the credal classifier COMP-AODE*, substituting the uniform prior by a set of priors. COMP-AODE* returns more classes when the classification is prior-dependent, namely if the most probable class varies with the prior adopted over the SPODEs. COMP-AODE* achieves higher classification utility than both COMP-AODE and AODE.

#### Likelihood-Based Robust Classification with Bayesian Networks

##### Antonucci, Alessandro and Cattaneo, Marco and Corani, Giorgio (2012).

In Greco, Salvatore and Bouchon-Meunier, Bernadette and Coletti, Giulianella and Fedrizzi, Mario and Matarazzo, Benedetto and Yager, Ronald R. (Eds),

*Advances in Computational Intelligence*. Catania, Italy , Jul 9-13, 2012. Communications in Computer and Information Science 299 , Springer , 491–500 .## BIB

@inproceedings{antonucci2012b, author = {Antonucci, Alessandro and Cattaneo, Marco and Corani, Giorgio}, booktitle = {Advances in Computational Intelligence}, address = {Catania, Italy}, eventdate = {Jul 9-13, 2012}, editor = {Greco, Salvatore and Bouchon-Meunier, Bernadette and Coletti, Giulianella and Fedrizzi, Mario and Matarazzo, Benedetto and Yager, Ronald R.}, pages = {491--500}, publisher = {Springer}, series = {Communications in Computer and Information Science}, title = {Likelihood-Based Robust Classification with Bayesian Networks}, volume = {299}, year = {2012} }

## ABS

Bayesian networks are commonly used for classification: a structural learning algorithm determines the network graph, while standard approaches estimate the model parameters from data. Yet, with few data the corresponding assessments can be unreliable. To gain robustness in this phase, we consider a likelihood-based learning approach, which takes all the model quantifications whose likelihood exceeds a given threshold. A new classification algorithm based on this approach is presented. Notably, this is a credal classifier, i.e., more than a single class can be returned in output. This is the case when the Bayesian networks consistent with the threshold constraint assign different class labels to a test instance. This is the first classifier of this kind for general topologies. Experiments show how this approach provide the desired robustness.

#### Active Learning by the Naive Credal Classifier

##### Antonucci, Alessandro and Corani, Giorgio and Gabaglio, Sandra (2012).

In Cano, A. and Gómez-Olmedo, M. and Nielsen, T.D. (Eds),

*Proceeding of the sixth European Workshop on Probabilistic Graphical Models (PGM 2012)*. Granada, Spain , Sep 19-21, 2012. PGM , 3–10 .## BIB

@inproceedings{antonucci2012c, author = {Antonucci, Alessandro and Corani, Giorgio and Gabaglio, Sandra}, booktitle = {Proceeding of the sixth European Workshop on Probabilistic Graphical Models (PGM 2012)}, editor = {Cano, A. and G\'omez-Olmedo, M. and Nielsen, T.D.}, eventdate = {Sep 19-21, 2012}, pages = {3--10}, publisher = {PGM}, title = {Active Learning by the Naive Credal Classifier}, address = {Granada, Spain}, year = {2012} }

## ABS

In standard classification a training set of supervised instances is given. In a more general setup, some supervised instances are available, while further ones should be chosen from an unsupervised set and then annotated. As the annotation step is costly, active learning algorithms are used to select which instances to annotate to maximally increase the classification performance while annotating only a limited number of them. Several active learning algorithms are based on the naive Bayes classifier. We work instead with the naive credal classifier, namely an extension of naive Bayes to imprecise probability. We propose two novel methods for active learning based on the naive credal classifier. Empirical comparisons show performance comparable or slightly superior to that of approaches solely based on the naive Bayes.

#### An Interval-Valued Dissimilarity Measure for Belief Functions Based on Credal Semantics

##### Antonucci, Alessandro (2012).

In Denoeux, T. and M.H., Masson (Eds),

*Belief Functions: Theory and Applications - Proceedings of the 2nd International Conference on Belief Functions*. Compiègne, France , 9-11 May, 2012. Advances in Soft Computing 164 , Springer , 37-44 .## BIB

@inproceedings{antonucci2012a, author = {Antonucci, Alessandro}, booktitle = {Belief Functions: Theory and Applications - Proceedings of the 2nd International Conference on Belief Functions}, doi = {https://doi.org/10.1007/978-3-642-29461-7_4}, editor = {Denoeux, T. and M.H., Masson}, eventdate = {9-11 May, 2012}, pages = {37-44}, publisher = {Springer}, series = {Advances in Soft Computing}, title = {An Interval-Valued Dissimilarity Measure for Belief Functions Based on Credal Semantics}, address = {Compi{\`e}gne, France}, volume = {164}, year = {2012}, bdsk-url-1 = {https://doi.org/10.1007/978-3-642-29461-7_4} }

## ABS

Evidence theory extends Bayesian probability theory by allowing for a more expressive model of subjective uncertainty. Besides standard interpretation of belief functions, where uncertainty corresponds to probability masses which might refer to whole subsets of the possibility space, credal semantics can be also considered. Accordingly, a belief function can be identified with the whole set of probability mass functions consistent with the beliefs induced by the masses. Following this interpretation, a novel, set-valued, dissimilarity measure with a clear behavioral interpretation can be defined. We describe the main features of this new measure and comment the relation with other measures proposed in the literature.

#### Decision Making by Credal Nets

##### Antonucci, Alessandro and de Campos, Cassio Polpo (2011).

In

*Proceedings of the International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC 2011)*. Hangzhou, China , Aug 26-27, 2011. Volume 1 , IEEE , 201-204 .## BIB

@inproceedings{antonucci2011d, author = {Antonucci, Alessandro and de Campos, Cassio Polpo}, booktitle = {Proceedings of the International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC 2011)}, eventdate = {Aug 26-27, 2011}, pages = {201-204}, publisher = {IEEE}, title = {Decision Making by Credal Nets}, address = {Hangzhou, China}, volume = {Volume 1}, year = {2011} }

## ABS

Credal nets are probabilistic graphical models which extend Bayesian nets to cope with sets of distributions. This feature makes the model particularly suited for the implementation of classifiers and knowledge-based systems. When working with sets of (instead of single) probability distributions, the identification of the optimal option can be based on different criteria, some of them eventually leading to multiple choices. Yet, most of the inference algorithms for credal nets are designed to compute only the bounds of the posterior probabilities. This prevents some of the existing criteria from being used. To overcome this limitation, we present two simple transformations for credal nets which make it possible to compute decisions based on the maximality and E-admissibility criteria without any modification in the inference algorithms. We also prove that these decision problems have the same complexity of standard inference, being NP^PP-hard for general credal nets and NP-hard for polytrees.

#### Likelihood-Based Naive Hierarchical Credal Classifier

##### Antonucci, Alessandro and Cattaneo, Marco and Corani, Giorgio (2011).

In Coolen, Frank and de Cooman, Gert and Fetz, Thomas and Oberguggenberger, Michael (Eds),

*ISIPTA ’11: Proceedings of the seventh International Symposium on Imprecise Probability: Theories and Applications*. Innsbruck, Austria , Jul 25-28, 2011. SIPTA , 21-30 .## BIB

@inproceedings{antonucci2011a, editor = {Coolen, Frank and de Cooman, Gert and Fetz, Thomas and Oberguggenberger, Michael}, author = {Antonucci, Alessandro and Cattaneo, Marco and Corani, Giorgio}, booktitle = {ISIPTA '11: Proceedings of the seventh International Symposium on Imprecise Probability: Theories and Applications}, eventdate = {Jul 25-28, 2011}, pages = {21-30}, publisher = {SIPTA}, title = {Likelihood-Based Naive Hierarchical Credal Classifier}, address = {Innsbruck, Austria}, year = {2011} }

## ABS

The naive credal classifier extends the classical naive Bayes classifier to imprecise probabilities, substituting the uniform prior by the imprecise Dirichlet model. As an alternative to the naive credal classifier, we present a hierarchical likelihood-based approach, which extends in a novel way the naive Bayes towards imprecise probabilities; in particular, it considers any possible quantification (each one defining a naive Bayes classifier) apart from those assigning to the available data a probability below a given threshold level. Besides the available supervised data, in the likelihood evaluation we also consider the instance to be classified, for which the value of the class variable is assumed missing-at-random. We obtain a closed formula to compute the dominance according to the maximality criterion for any threshold level. As there are currently no well-established metrics for comparing credal classifiers which have considerably different determinacy, we compare the two classifiers when they have comparable determinacy, finding that in those cases they generate almost equivalent classifications.

#### Action Recognition by Imprecise Hidden Markov Models

##### Antonucci, Alessandro and de Rosa, Rocco and Giusti, Alessandro (2011).

In

*Proceedings of the 2011 International Conference on Image Processing, Computer Vision and Pattern Recognition, IPCV 2011*. Las Vegas, Nevada, USA , Jul 18-21, 2011. CSREA Press , 474-478 .## BIB

@inproceedings{antonucci2011b, author = {Antonucci, Alessandro and de Rosa, Rocco and Giusti, Alessandro}, booktitle = {Proceedings of the 2011 International Conference on Image Processing, Computer Vision and Pattern Recognition, IPCV 2011}, eventdate = {Jul 18-21, 2011}, pages = {474-478}, publisher = {CSREA Press}, title = {Action Recognition by Imprecise Hidden Markov Models}, address = {Las Vegas, Nevada, USA}, year = {2011} }

## ABS

Hidden Markov models (HMMs) are powerful tools to capture the dynamics of a human action by providing a sufficient level of abstraction to recognise what two video sequences, depicting the same kind of action, have in common. If the sequence is short and hence only few data are available, the EM algorithm, which is generally employed to learn HMMs, might return unreliable estimates. As a possible solution to this problem, a robust version of the EM algorithm, which provides an interval-valued quantification of the HMM probabilities is provided. This takes place in an imprecise-probabilistic framework, where action recognition can be based on the (bounds of the) likelihood assigned by an imprecise HMM to the considered video sequence. Experiments show that this approach is quite effective in discriminating the hard-to-recognise sequences from the easy ones. In practice, either the recognition algorithm returns a set of action labels, which typically includes the right one, either a single answer, which is very likely to be correct, is provided.

#### The Imprecise Noisy-OR Gate

##### Antonucci, Alessandro (2011).

In

*FUSION 2011: Proceedings of the 14th International Conference on Information Fusion*. Chicago, Illinois, USA , Jul 5-8, 2011. IEEE , 709-715 .## BIB

@inproceedings{antonucci2011c, author = {Antonucci, Alessandro}, booktitle = {FUSION 2011: Proceedings of the 14th International Conference on Information Fusion}, eventdate = {Jul 5-8, 2011}, pages = {709-715}, publisher = {IEEE}, title = {The Imprecise Noisy-OR Gate}, address = {Chicago, Illinois, {USA}}, year = {2011} }

## ABS

The noisy-OR gate is an important tool for a compact elicitation of the conditional probabilities of a Bayesian network. An imprecise-probabilistic version of this model, where sets instead of single distributions are used to model uncertainty about the inhibition of the causal factors, is proposed. This transforms the original Bayesian network into a so-called credal network. Despite the higher computational complexity generally characterizing inference on credal networks, it is possible to prove that, exactly as for Bayesian networks, the local complexity to update probabilities on an imprecise noisy-OR gate takes only linear, instead of exponential, time in the number of causes. This result is also extended to fault tree analysis and allows for a fast fusion of the causal effects on models with an imprecise-probabilistic quantification of the initiating events.

#### Generalized Loopy 2U: A New Algorithm for Approximate Inference in Credal Networks

##### Antonucci, Alessandro and Yi, Sun and de Campos, Cassio Polpo and Zaffalon, Marco (2010).

*International Journal of Approximate Reasoning***55**(5) , 474–484.## BIB

@article{antonucci2009b, author = {Antonucci, Alessandro and Yi, Sun and de Campos, Cassio Polpo and Zaffalon, Marco}, date-modified = {2019-12-29 21:24:38 +0200}, journal = {International Journal of Approximate Reasoning}, number = {5}, pages = {474--484}, title = {Generalized Loopy {2U}: A New Algorithm for Approximate Inference in Credal Networks}, volume = {55}, year = {2010} }

## ABS

Credal networks generalize Bayesian networks by relaxing the requirement of precision of probabilities. Credal networks are considerably more expressive than Bayesian networks, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal networks. The algorithm is based on an important representation result we prove for general credal networks: that any credal network can be equivalently reformulated as a credal network with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal network is then updated by L2U, a loopy approximate algorithm for binary credal networks. Overall, we generalize L2U to non-binary credal networks, obtaining a scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences with respect to other state-of-the-art algorithms is evaluated by extensive numerical tests.

#### An Aggregation Framework Based on Coherent Lower Previsions: Application to Zadeh’s Paradox and Sensor Networks

##### Benavoli, Alessio and Antonucci, Alessandro (2010).

*International Journal of Approximate Reasoning***51**(9) , 1014–1028.## BIB

@article{benavoli2010a, author = {Benavoli, Alessio and Antonucci, Alessandro}, date-modified = {2019-12-29 21:24:00 +0200}, journal = {International Journal of Approximate Reasoning}, number = {9}, pages = {1014--1028}, title = {An Aggregation Framework Based on Coherent Lower Previsions: Application to {Z}adeh's Paradox and Sensor Networks}, volume = {51}, year = {2010} }

## ABS

The problem of aggregating two or more sources of information containing knowl- edge about a common domain is considered. We propose an aggregation frame- work for the case where the available information is modelled by coherent lower previsions, corresponding to convex sets of probability mass functions. The con- sistency between aggregated beliefs and sources of information is discussed. A closed formula, which specializes our rule to a particular class of models, is also derived. Two applications consisting in a possible explanation of Zadeh’s paradox and an algorithm for estimation fusion in sensor networks are finally reported.

#### Credal Sets Approximation by Lower Probabilities: Application to Credal Networks

##### Antonucci, Alessandro and Cuzzolin, Fabio (2010).

In Hüllermeier, E. and Kruse, R. and Hoffmann, F. (Eds),

*Computational Intelligence for Knowledge-Based Systems Design, 13th International Conference on Information Processing and Management of Uncertainty, IPMU 2010*. Dortmund, Germany , Jun 28 - Jul 2, 2010. Lecture Notes in Computer Science 6178 , Springer , 716-725 .## BIB

@inproceedings{antonucci2010a, author = {Antonucci, Alessandro and Cuzzolin, Fabio}, booktitle = {Computational Intelligence for Knowledge-Based Systems Design, 13th International Conference on Information Processing and Management of Uncertainty, IPMU 2010}, editor = {H\"ullermeier, E. and Kruse, R. and Hoffmann, F.}, eventdate = {Jun 28 - Jul 2, 2010}, pages = {716-725}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Credal Sets Approximation by Lower Probabilities: Application to Credal Networks}, address = {Dortmund, Germany}, volume = {6178}, year = {2010} }

## ABS

Credal sets are closed convex sets of probability mass functions. The lower probabilities specified by a credal set for each element of the power set can be used as constraints defining a second credal set. This simple procedure produces an outer approximation, with a bounded number of extreme points, for general credal sets. The approximation is optimal in the sense that no other lower probabilities can specify smaller supersets of the original credal set. Notably, in order to be computed, the approximation does not need the extreme points of the credal set, but only its lower probabilities. This makes the approximation particularly suited for credal networks, which are a generalization of Bayesian networks based on credal sets. Although most of the algorithms for credal networks updating only return lower posterior probabilities, the suggested approximation can be used to evaluate (as an outer approximation of) the posterior credal set. This makes it possible to adopt more sophisticated decision making criteria, without having to replace existing algorithms. The quality of the approximation is investigated by numerical tests.

#### Epistemic Irrelevance in Credal Nets: The Case of Imprecise Markov trees

##### de Cooman, Gert and Hermans, Filip and Antonucci, Alessandro and Zaffalon, Marco (2010).

*International Journal of Approximate Reasoning***51**(9) , 1029–1052.## BIB

@article{decooman2010a, author = {de Cooman, Gert and Hermans, Filip and Antonucci, Alessandro and Zaffalon, Marco}, date-modified = {2019-12-29 12:12:11 +0200}, journal = {International Journal of Approximate Reasoning}, number = {9}, pages = {1029--1052}, title = {Epistemic Irrelevance in Credal Nets: The Case of Imprecise {M}arkov trees}, volume = {51}, year = {2010} }

## ABS

We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is arguably more suited for a behavioural theory of probability. Focusing on directed trees, we show how to combine the given local uncertainty models in the nodes of the graph into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is linear in the number of nodes, is formulated entirely in terms of coherent lower previsions, and is shown to satisfy a number of rationality requirements. We supply examples of the algorithm’s operation, and report an application to on-line character recognition that illustrates the advantages of our approach for prediction. We comment on the perspectives, opened by the availability, for the first time, of a truly efficient algorithm based on epistemic irrelevance.

#### Building Knowledge-based Expert Systems: A Tutorial

##### Piatti, Alberto and Antonucci, Alessandro and Zaffalon, Marco (2010).

In Baswell, A.R. (Eds),

*Advances in Mathematics Research*. Nova Science Publishers .## BIB

@inbook{piatti2010a, address = {New York}, author = {Piatti, Alberto and Antonucci, Alessandro and Zaffalon, Marco}, booktitle = {Advances in Mathematics Research}, chapter = {2}, date-modified = {2019-12-29 12:18:11 +0200}, editor = {Baswell, A.R.}, publisher = {Nova Science Publishers}, title = {Building Knowledge-based Expert Systems: A Tutorial}, volume = {11}, year = {2010} }

## ABS

Knowledge-based systems are computer programs achieving expert-level competence in solving problems for specific task areas. This chapter is a tutorial on the construction of knowledge-based systems in the theoretical framework of credal networks. Credal networks are a generalization of Bayesian networks where credal sets, i.e., closed convex sets of probability measures, are used instead of precise probabilities. This allows for a more flexible process of elicitation than in the case of Bayesian networks. In fact, credal sets allow to represent ambiguity, contrast and contradiction in a natural and realistic way. The procedure we propose is based on a sharp distinction between the domain knowledge and the process linking this knowledge to the perceived evidence, which we call the observational process. This distinction leads to a very flexible representation of both domain knowledge and knowledge about the way the information is collected, together with a procedure of aggregation of the information coming from the different sources. The overall procedure is illustrated along the chapter by a simple knowledge-based system for the prediction of the result of a football match.

#### Multiple Model Tracking by Imprecise Markov Trees

##### Antonucci, Alessandro and Benavoli, Alessio and Zaffalon, Marco and de Cooman, Gert and Hermans, Filip (2009).

In

*FUSION 2009: Proceedings of the 12th International Conference on Information Fusion*. Seattle, Washington, USA , Jul 6-9, 2009. IEEE .## BIB

@inproceedings{antonucci2009c, author = {Antonucci, Alessandro and Benavoli, Alessio and Zaffalon, Marco and de Cooman, Gert and Hermans, Filip}, booktitle = {FUSION 2009: Proceedings of the 12th International Conference on Information Fusion}, date-modified = {2019-12-29 12:16:20 +0200}, eventdate = {Jul 6-9, 2009}, month = jul, publisher = {IEEE}, title = {Multiple Model Tracking by Imprecise {M}arkov Trees}, address = {Seattle, Washington, {USA}}, year = {2009} }

## ABS

We present a new procedure for tracking manoeuvring objects by hidden Markov chains. It leads to more reliable modelling of the transitions between hidden states compared to similar approaches proposed within the Bayesian framework: we adopt convex sets of probability mass functions rather than single ’precise probability’ specifications, in order to provide a more realistic and cautious model of the manoeuvre dynamics. In general, the downside of such increased freedom in the modelling phase is a higher inferential complexity. However, the simple topology of hidden Markov chains allows for efficient tracking of the object through a recently developed belief propagation algorithm. Furthermore, the imprecise specification of the transitions can produce so-called indecision, meaning that more than one model may be suggested by our method as a possible explanation of the target kinematics. In summary, our approach leads to a multiple-model estimator whose performance, investigated through extensive numerical tests, turns out to be more accurate and robust than that of Bayesian ones.

#### Aggregating Imprecise Probabilistic Knowledge

##### Benavoli, Alessio and Antonucci, Alessandro (2009).

In Augustin, Thomas and Coolen, Frank and Moral, Serafín and Troffaes, Matthias C.M. (Eds),

*Proceedings of the Sixth International Symposium on Imprecise Probability: Theories and Applications (ISIPTA ’09)*. Durham, United Kingdom , Jul 14-18, 2009. SIPTA , 31–40 .## BIB

@inproceedings{benavoli2009a, address = {Durham, United Kingdom}, author = {Benavoli, Alessio and Antonucci, Alessandro}, booktitle = {Proceedings of the Sixth International Symposium on Imprecise Probability: Theories and Applications (ISIPTA '09)}, editor = {Augustin, Thomas and Coolen, Frank and Moral, Serafín and Troffaes, Matthias C.M.}, eventdate = {Jul 14-18, 2009}, month = jul, pages = {31--40}, publisher = {SIPTA}, title = {Aggregating Imprecise Probabilistic Knowledge}, year = {2009} }

## ABS

The problem of aggregating two or more sources of information containing knowledge about a same domain is considered. We propose an aggregation rule for the case where the available information is modeled by coherent lower previsions, corresponding to convex sets of probability mass functions. The consistency between aggregated beliefs and sources of information is discussed. A closed formula, which specializes our rule to a particular class of models, is also derived. Finally, an alternative explanation of Zadeh’s paradox is provided.

#### Epistemic Irrelevance in Credal Networks: The Case of Imprecise Markov Trees

##### de Cooman, Gert and Hermans, Filip and Antonucci, Alessandro and Zaffalon, Marco (2009).

In

*ISIPTA ’09: Proceedings of the Sixth International Symposium on Imprecise Probability: Theories and Applications*. Durham, United Kingdom , Jul 14-18, 2009. SIPTA , 149–158 .## BIB

@inproceedings{decooman2009a, address = {Durham, United Kingdom}, author = {de Cooman, Gert and Hermans, Filip and Antonucci, Alessandro and Zaffalon, Marco}, booktitle = {ISIPTA '09: Proceedings of the Sixth International Symposium on Imprecise Probability: Theories and Applications}, date-modified = {2019-12-29 12:12:25 +0200}, editor = {}, eventdate = {Jul 14-18, 2009}, pages = {149--158}, publisher = {SIPTA}, title = {Epistemic Irrelevance in Credal Networks: The Case of Imprecise {M}arkov Trees}, year = {2009} }

## ABS

We replace strong independence in credal networks with the weaker notion of epistemic irrelevance. Focusing on directed trees, we show how to combine local credal sets into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is essentially linear in the number of nodes, is formulated entirely in terms of coherent lower previsions. We supply examples of the algorithm’s operation, and report an application to on-line character recognition that illustrates the advantages of our model for prediction.

#### Credal Networks for Military Identification Problems

##### Antonucci, Alessandro and Brühlmann, Ralph and Piatti, Alberto and Zaffalon, Marco (2009).

*International Journal of Approximate Reasoning***50**(2) , 666–679.## BIB

@article{antonucci2009a, author = {Antonucci, Alessandro and Br{\"u}hlmann, Ralph and Piatti, Alberto and Zaffalon, Marco}, date-modified = {2019-12-29 12:47:40 +0200}, journal = {International Journal of Approximate Reasoning}, number = {2}, pages = {666--679}, title = {Credal Networks for Military Identification Problems}, volume = {50}, year = {2009} }

## ABS

Credal networks are imprecise probabilistic graphical models generalizing Bayesian networks to convex sets of probability mass functions. This makes credal networks particularly suited to model expert knowledge under very general conditions, including states of qualitative and incomplete knowledge. In this paper, we present a credal network for risk evaluation in case of intrusion of civil aircrafts into a restricted flight area. The different factors relevant for this evaluation, together with an independence structure over them, are initially identified. These factors are observed by sensors, whose reliabilities can be affected by variable external factors, and even by the behaviour of the intruder. A model of these observation processes, and the necessary fusion scheme for the information returned by the sensors measuring the same factor, are both completely embedded into the structure of the credal network. A pool of experts, facilitated in their task by specific techniques to convert qualitative judgements into imprecise probabilistic assessments, has made possible the quantification of the network. We show the capabilities of the proposed model by means of some preliminary tests referred to simulated scenarios. Overall, we can regard this application as a useful tool to support military experts in their decision, but also as a quite general imprecise-probability paradigm for information fusion.

#### Modeling Unreliable Observations in Bayesian Networks by Credal Networks

##### Antonucci, Alessandro and Piatti, Alberto (2009).

In Godo, L. and Pugliese, A. (Eds),

*Scalable Uncertainty Management, Third International Conference, SUM 2009*. Washington, D.C., USA , Sep 28-30 2009. Lecture Notes in Computer Science 5785 , Springer , 28–39 .## BIB

@inproceedings{piatti2008a, author = {Antonucci, Alessandro and Piatti, Alberto}, booktitle = {Scalable Uncertainty Management, Third International Conference, SUM 2009}, date-modified = {2019-12-29 12:16:26 +0200}, editor = {Godo, L. and Pugliese, A.}, eventdate = {Sep 28-30 2009}, pages = {28--39}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Modeling Unreliable Observations in Bayesian Networks by Credal Networks}, address = {Washington, D.C., USA}, volume = {5785}, year = {2009} }

## ABS

Bayesian networks are probabilistic graphical models widely employed in AI for the implementation of knowledge-based systems. Standard inference algorithms can update the beliefs about a variable of interest in the network after the observation of some other variables. This is usually achieved under the assumption that the observations could reveal the actual states of the variables in a fully reliable way. We propose a procedure for a more general modeling of the observations, which allows for updating beliefs in different situations, including various cases of unreliable, incomplete, uncertain and also missing observations. This is achieved by augmenting the original Bayesian network with a number of auxiliary variables corresponding to the observations. For a flexible modeling of the observational process, the quantification of the relations between these auxiliary variables and those of the original Bayesian network is done by credal sets, i.e., convex sets of probability mass functions. Without any lack of generality, we show how this can be done by simply estimating the bounds for the likelihoods of the observations. Overall, the Bayesian network is transformed into a credal network, for which a standard updating problem has to be solved. Finally, a number of transformations that might simplify the updating of the resulting credal network is provided.

#### Imprecise Probabilistic Graphical Models: Equivalent Representations, Inference Algorithms and Applications

##### Antonucci, Alessandro (2008).

Ph.D. Thesis, Università della Svizzera Italiana.

## BIB

@phdthesis{antonucci2008c, author = {Antonucci, Alessandro}, month = apr, school = {Universit\`a della Svizzera Italiana}, title = {Imprecise Probabilistic Graphical Models: Equivalent Representations, Inference Algorithms and Applications}, url = {http://doc.rero.ch/record/10745?ln=en}, year = {2008}, bdsk-url-1 = {http://doc.rero.ch/record/10745?ln=en} }

## ABS

Credal networks are probabilistic graphical models that extend Bayesian nets to deal with imprecision in probability, and can actually be regarded as sets of Bayesian nets. Credal nets appear to be powerful means to represent and deal with many important and challenging problems in uncertain reasoning. The counterpart of having more freedom in the modeling phase is an increased inferential complexity of inferences, e.g., the so-called belief updating becomes a hard task even on relatively simple topologies. In this thesis, I start my investigation on credal networks by considering equivalent representations of those models. More specifically, I first deliver a new graphical language, which is called decision-theoretic being inspired by the formalism of decision graphs, for a unified representation of credal networks of any kind. I also present another representation, which is called binarization, being in fact a reformulation of a credal network solely based on binary variables. Remarkably, I prove that if a credal net is first reformulated by its decision-theoretic representation and then by the corresponding binarization, the resulting representation is completely equivalent. An equivalence relation between Bayesian and credal nets, when the reason for the missingness of some of the variables in the Bayesian nets is unknown, is also provided. The developed equivalent representations are applied to inference problems. First, I show that, by a decision-theoretic formulation, the algorithms that have been already designed for credal networks, which are mostly referred to a specific class of models, called separately specified nets, can be generalized to credal networks of any kind. Similar formalisms are also employed to solve inference and classification problems with missing observations. I also present a state-ofthe- art updating algorithm which is based on the equivalent binary representation. This algorithm, called GL2U, offers an efficient procedure for approximate updating of general credal nets. The quality of the overall approximation is investigated by promising numerical experiments. As a further theoretical investigation, I consider a classification problem for Bayesian networks for which a hardness proof together with a fast algorithm for a subclass of models is provided. Finally, two real-world applications of credal networks are presented. First, I consider a military identification problem, consisting in the detection of the goal of an intruder entering a no-fly area. The problem, together with the necessary fusion of the information gathered by the sensors is mapped by our techniques into a credal network updating task. The solution is then obtained by the GL2U algorithm. The second application is an environmental model for hazard assessment of debris flows by credal networks. A credal network evaluates the level of risk, corresponding to the observed values of the triggering factors, for this specific natural hazard. For some factors, whose observations are more difficult, the corresponding soft evidential information is embedded by our formalism into the structure of the network. This model is employed for extensive numerical analysis on the Swiss territory.

#### Generalized Loopy 2U: A New Algorithm for Approximate Inference in Credal Networks

##### Antonucci, Alessandro and Zaffalon, Marco and Yi, Sun and de Campos, Cassio Polpo (2008).

In Jaeger, M. and Nielsen, T. D. (Eds),

*PGM’08: Proceedings of the Fourth European Workshop on Probabilistic Graphical Models*. Hirtshals, Denmark , Sep 17-19, 2008. PGM , 17–24 .## BIB

@inproceedings{antonucci2008a, author = {Antonucci, Alessandro and Zaffalon, Marco and Yi, Sun and de Campos, Cassio Polpo}, booktitle = {PGM'08: Proceedings of the Fourth European Workshop on Probabilistic Graphical Models}, editor = {Jaeger, M. and Nielsen, T. D.}, eventdate = {Sep 17-19, 2008}, pages = {17--24}, title = {Generalized Loopy {2U}: A New Algorithm for Approximate Inference in Credal Networks}, address = {Hirtshals, Denmark}, publisher = {PGM}, year = {2008} }

## ABS

Credal nets generalize Bayesian nets by relaxing the requirement of precision of probabilities. Credal nets are considerably more expressive than Bayesian nets, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal nets. The algorithm is based on an important representation result we prove for general credal nets: that any credal net can be equivalently reformulated as a credal net with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal net is updated by L2U, a loopy approximate algorithm for binary credal nets. Thus, we generalize L2U to non-binary credal nets, obtaining an accurate and scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences is evaluated by empirical tests.

#### Decision-Theoretic Specification of Credal Networks: A Unified Language for Uncertain Modeling with Sets of Bayesian Networks

##### Antonucci, Alessandro and Zaffalon, Marco (2008).

*International Journal of Approximate Reasoning***49**(2) , 345–361.## BIB

@article{antonucci2008b, author = {Antonucci, Alessandro and Zaffalon, Marco}, journal = {International Journal of Approximate Reasoning}, number = {2}, pages = {345--361}, title = {Decision-Theoretic Specification of Credal Networks: A Unified Language for Uncertain Modeling with Sets of Bayesian Networks}, volume = {49}, year = {2008} }

## ABS

Credal networks are models that extend Bayesian nets to deal with imprecision in probability, and can actually be regarded as sets of Bayesian nets. Credal nets appear to be powerful means to represent and deal with many important and challenging problems in uncertain reasoning. We give examples to show that some of these problems can only be modeled by credal nets called non-separately specified. These, however, are still missing a graphical representation language and updating algorithms. The situation is quite the opposite with separately specified credal nets, which have been the subject of much study and algorithmic development. This paper gives two major contributions. First, it delivers a new graphical language to formulate any type of credal network, both separately and non-separately specified. Second, it shows that any non-separately specified net represented with the new language can be easily transformed into an equivalent separately specified net, defined over a larger domain. This result opens up a number of new outlooks and concrete outcomes: first of all, it immediately enables the existing algorithms for separately specified credal nets to be applied to non-separately specified ones. We explore this possibility for the 2U algorithm: an algorithm for exact updating of singly connected credal nets, which is extended by our results to a class of non-separately specified models. We also consider the problem of inference on Bayesian networks, when the reason that prevents some of the variables from being observed is unknown. The problem is first reformulated in the new graphical language, and then mapped into an equivalent problem on a separately specified net. This provides a first algorithmic approach to this kind of inference, which is also proved to be NP-hard by similar transformations based on our formalism.

#### Spatially Distributed Identification of Debris Flow Source Areas by Credal Networks

##### Salvetti, Andrea and Antonucci, Alessandro and Zaffalon, Marco (2008).

In Sànchez-Marrè, M. and Béjar, J. and Comas, J. and Rizzoli, A. E. and Guariso, G. (Eds),

*iEMSs 2008: International Congress on Environmental Modelling and Software Integrating Sciences and Information Technology for Environmental Assessment and Decision Making (Transactions of the 4th Biennial Meeting of the International Environmental Modelling and Software Society)*. Barcelona, Catalonia , Jul 2008. iEMSs , 380–387 .## BIB

@inproceedings{salvetti2008a, author = {Salvetti, Andrea and Antonucci, Alessandro and Zaffalon, Marco}, title = {Spatially Distributed Identification of Debris Flow Source Areas by Credal Networks}, year = {2008}, address = {Barcelona, Catalonia}, booktitle = {iEMSs 2008: International Congress on Environmental Modelling and Software Integrating Sciences and Information Technology for Environmental Assessment and Decision Making (Transactions of the 4th Biennial Meeting of the International Environmental Modelling and Software Society)}, date-modified = {2019-12-29 12:14:55 +0200}, editor = {S{\`a}nchez-Marr{\`e}, M. and B{\'e}jar, J. and Comas, J. and Rizzoli, A. E. and Guariso, G.}, eventdate = {Jul 2008}, pages = {380--387}, publisher = {iEMSs} }

## ABS

Debris flows represent a very destructive natural hazard, affecting buildings, transport infrastructures, and, very often, causing human losses in mountain regions. That makes the identification of potential source areas of debris flows inside a watershed particularly important. In this paper we present a general identification procedure based on the credal network (that is an imprecise probabilistic graphical model generalizing Bayesian networks) originally introduced by Antonucci et al. (2004). That model is significantly improved by a more refined description of the meteorological and hydrological processes contributing to the debris flow initiation. As a counterpart of such improvement, the model pays a slight increase in terms of computational time for identifications. That does not prevent its extensive, spatially distributed, application to whole basins, thanks to a preliminary deterministic analysis that rejects local areas where the triggering of a debris flow cannot take place. The overall procedure is tested for a debris flow prone watershed in Southern Switzerland. The model detects the areas in the basin more prone to debris flow initiation and also shows that different rainfall return periods produce different patterns of hazard in the basin. That makes it possible with this procedure to determine the return period of the critical rainfall that triggers debris flow as a result of channel-bed failure in a specific point along the drainage network.

#### Credal Networks for Military Identification Problems

##### Antonucci, Alessandro and Brühlmann, Ralph and Piatti, Alberto and Zaffalon, Marco (2007).

In de Cooman, Gert and Vejnarová, Jirina and Zaffalon, Marco (Eds),

*ISIPTA ’07: Proceedings of the fifth International Symposium on on Imprecise Probability: Theories and Applications*. Prague, Czech Republic , Jul 16-19, 2007. Action M Agency , 1–10 .## BIB

@inproceedings{antonucci2007b, author = {Antonucci, Alessandro and Br{\"u}hlmann, Ralph and Piatti, Alberto and Zaffalon, Marco}, booktitle = {ISIPTA '07: Proceedings of the fifth International Symposium on on Imprecise Probability: Theories and Applications}, date-modified = {2019-12-29 12:49:56 +0200}, editor = {de Cooman, Gert and Vejnarov\'a, Jirina and Zaffalon, Marco}, eventdate = {Jul 16-19, 2007}, pages = {1--10}, publisher = {Action M Agency}, title = {Credal Networks for Military Identification Problems}, address = {Prague, Czech Republic}, year = {2007} }

## ABS

Credal networks are imprecise probabilistic graphical models generalizing Bayesian networks to convex sets of probability mass functions. This makes credal networks particularly suited to capture and model expert knowledge under very general conditions, including states of qualitative and incomplete knowledge. In this paper, we present a credal network for risk evaluation in case of intrusion of civil aircrafts into a no-fly zone. The different factors relevant for this evaluation, together with an independence structure over them, are initially identified. These factors are observed by sensors, whose reliabilities can be affected by variable external factors, and even by the behavior of the intruder. A model of these observation mechanisms, and the necessary fusion scheme for the information returned by the sensors measuring the same factor, are both completely embedded into the structure of the credal network. A pool of experts, facilitated in their task by specific techniques to convert qualitative judgments into imprecise probabilistic assessments, has made possible the quantification of the network. We show the capabilities of the proposed network by means of some preliminary tests referred to simulated scenarios. Overall, we can regard this application as an useful tool to support military experts in their decision, but also as a quite general imprecise-probability paradigm for information fusion.

#### Credal Networks for Operational Risk Measurement and Management

##### Antonucci, Alessandro and Piatti, Alberto and Zaffalon, Marco (2007).

In Apolloni, B. and Howlett, R. J. and Jain, L. C. (Eds),

*Proceedings of the 11th International Conference on Knowledge-Based and Intelligent Information & Engineering Systems: KES2007, Lectures Notes in Computer Science*. Vietri sul Mare, Italy , Sep 12-14, 2007. 4693 , Springer , 604–611 .## BIB

@inproceedings{antonucci2007c, author = {Antonucci, Alessandro and Piatti, Alberto and Zaffalon, Marco}, booktitle = {Proceedings of the 11th International Conference on Knowledge-Based and Intelligent Information \& Engineering Systems: KES2007, Lectures Notes in Computer Science}, editor = {Apolloni, B. and Howlett, R. J. and Jain, L. C.}, eventdate = {Sep 12-14, 2007}, pages = {604--611}, publisher = {Springer}, title = {Credal Networks for Operational Risk Measurement and Management}, address = {Vietri sul Mare, Italy}, volume = {4693}, year = {2007} }

## ABS

According to widely accepted guidelines for self-regulation, the capital requirements of a bank should relate to the level of risk with respect to three different categories. Among them, operational risk is the more difficult to assess, as it requires merging expert judgments and quantitative information about the functional structure of the bank. A number of approaches to the evaluation of operational risk based on Bayesian networks have been recently considered. In this paper, we propose credal networks, which are a generalization of Bayesian networks to imprecise probabilities, as a more appropriate framework for the measurement and management of operational risk. The reason is the higher flexibility provided by credal networks compared to Bayesian networks in the quantification of the probabilities underlying the model: this makes it possible to represent human expertise required for these evaluations in a credible and robust way. We use a real-world application to demonstrate these features and to show how to measure operational risk by means of algorithms for inference over credal nets. This is shown to be possible, also in the case when the observation of some factor is vague.

#### Credal Networks for Hazard Assessment of Debris Flows

##### Antonucci, Alessandro and Salvetti, Andrea and Zaffalon, Marco (2007).

In Kropp, Jürgen and Scheffran, Jürgen (Eds),

*Progress of Artificial Intelligence in Sustainability Science*. New York. Nova Science , 125–132 .## BIB

@inbook{antonucci2007d, location = {New York}, author = {Antonucci, Alessandro and Salvetti, Andrea and Zaffalon, Marco}, booktitle = {Progress of Artificial Intelligence in Sustainability Science}, pages = {125--132}, editor = {Kropp, Jürgen and Scheffran, Jürgen}, publisher = {Nova Science}, title = {Credal Networks for Hazard Assessment of Debris Flows}, year = {2007} }

#### Fast Algorithms for Robust Classification with Bayesian Nets

##### Antonucci, Alessandro and Zaffalon, Marco (2007).

*International Journal of Approximate Reasoning***44**(3) , 200–223.## BIB

@article{antonucci2007a, author = {Antonucci, Alessandro and Zaffalon, Marco}, journal = {International Journal of Approximate Reasoning}, number = {3}, pages = {200--223}, title = {Fast Algorithms for Robust Classification with {B}ayesian Nets}, volume = {44}, year = {2007} }

## ABS

We focus on a well-known classification task with expert systems based on Bayesian networks: predicting the state of a target variable given an incomplete observation of the other variables in the network, i.e., an observation of a subset of all the possible variables. To provide conclusions robust to near-ignorance about the process that prevents some of the variables from being observed, it has recently been derived a new rule, called conservative updating. With this paper we address the problem to efficiently compute the conservative updating rule for robust classification with Bayesian networks. We show first that the general problem is NP-hard, thus establishing a fundamental limit to the possibility to do robust classification efficiently. Then we define a wide subclass of Bayesian networks that does admit efficient computation. We show this by developing a new classification algorithm for such a class, which extends substantially the limits of efficient computation with respect to the previously existing algorithm. The algorithm is formulated as a variable elimination procedure, whose computation time is linear in the input size.

#### Binarization Algorithms for Approximate Updating in Credal Nets

##### Antonucci, Alessandro and Zaffalon, Marco and Ide, Jaime S. and Cozman, Fabio Gagliardi (2006).

In Penserini, Loris and Peppas, Pavlos and Perini, Anna (Eds),

*STAIRS’06: Proceedings of the third European Starting AI Researcher Symposium*. Riva del Garda, Italy , Aug 28, 2006. IOS Press , 120–131 .## BIB

@inproceedings{antonucci2006b, address = {Riva del Garda, Italy}, author = {Antonucci, Alessandro and Zaffalon, Marco and Ide, Jaime S. and Cozman, Fabio Gagliardi}, booktitle = {STAIRS'06: Proceedings of the third European Starting AI Researcher Symposium}, editor = {Penserini, Loris and Peppas, Pavlos and Perini, Anna}, month = aug, eventdate = {Aug 28, 2006}, pages = {120--131}, publisher = {IOS Press}, title = {Binarization Algorithms for Approximate Updating in Credal Nets}, year = {2006} }

## ABS

Credal networks generalize Bayesian networks relaxing numerical parameters. This considerably expands expressivity, but makes belief updating a hard task even on polytrees. Nevertheless, if all the variables are binary, polytree-shaped credal networks can be efficiently updated by the 2U algorithm. In this paper we present a binarization algorithm, that makes it possible to approximate an updating problem in a credal net by a corresponding problem in a credal net over binary variables. The procedure leads to outer bounds for the original problem. The binarized nets are in general multiply connected, but can be updated by the loopy variant of 2U. The quality of the overall approximation is investigated by promising numerical experiments.

#### Equivalence between Bayesian and Credal Nets on an Updating Problem

##### Antonucci, Alessandro and Zaffalon, Marco (2006).

In Lawry, J. and Miranda, E. and Bugarin, A. and Li, S. and Gil, M. A. and Grzegorzewski, P. and Hryniewicz, O. (Eds),

*Proceedings of third international conference on Soft Methods in Probability and Statistics (SMPS-2006)*. Bristol, United Kingdom , Sep 5-7, 2006. Springer , 223–230 .## BIB

@inproceedings{antonucci2006a, author = {Antonucci, Alessandro and Zaffalon, Marco}, booktitle = {Proceedings of third international conference on {S}oft {M}ethods in {P}robability and {S}tatistics ({SMPS}-2006)}, editor = {Lawry, J. and Miranda, E. and Bugarin, A. and Li, S. and Gil, M. A. and Grzegorzewski, P. and Hryniewicz, O.}, eventdate = {Sep 5-7, 2006}, pages = {223--230}, publisher = {Springer}, title = {Equivalence between {B}ayesian and Credal Nets on an Updating Problem}, address = {Bristol, United Kingdom}, year = {2006} }

## ABS

We establish an intimate connection between Bayesian and credal nets. Bayesian nets are precise graphical models, credal nets extend Bayesian nets to imprecise probability. We focus on traditional belief updating with credal nets, and on the kind of belief updating that arises with Bayesian nets when the reason for the missingness of some of the unobserved variables in the net is unknown. We show that the two updating problems are formally the same.

#### Locally Specified Credal Networks

##### Antonucci, Alessandro and Zaffalon, Marco (2006).

In Studený, M. and Vomlel, J. (Eds),

*PGM’06: Proceedings of the third European Workshop on Probabilistic Graphical Models*. Prague, Czech Republic , Sep 12-15, 2006. Action M Agency , 25–34 .## BIB

@inproceedings{antonucci2006c, address = {Prague, Czech Republic}, author = {Antonucci, Alessandro and Zaffalon, Marco}, booktitle = {PGM'06: Proceedings of the third European Workshop on Probabilistic Graphical Models}, editor = {Studen\'y, M. and Vomlel, J.}, eventdate = {Sep 12-15, 2006}, pages = {25--34}, publisher = {Action M Agency}, title = {Locally Specified Credal Networks}, year = {2006} }

## ABS

Credal networks are models that extend Bayesian nets to deal with imprecision in probability, and can actually be regarded as sets of Bayesian nets. Evidence suggests that credal nets are a powerful means to represent and deal with many important and challenging problems in uncertain reasoning. We give examples to show that some of these problems can only be modelled by credal nets called non-separately specified. These, however, are still missing a graphical representation language and solution algorithms. The situation is quite the opposite with separately specified credal nets, which have been the subject of much study and algorithmic development. This paper gives two major contributions. First, it delivers a new graphical language to formulate any type of credal network, both separately and non-separately specified. Second, it shows that any non-separately specified net represented with the new language can be easily transformed into an equivalent separately specified net, defined over a larger domain. This result opens up a number of new perspectives and concrete outcomes: first of all, it immediately enables the existing algorithms for separately specified credal nets to be applied to non-separately specified ones.

#### Fast Algorithms for Robust Classification with Bayesian Nets

##### Antonucci, Alessandro and Zaffalon, Marco (2005).

In Cozman, Fabio Gagliardi and Nau, Robert and Seidenfeld, Teddy (Eds),

*ISIPTA ’06: Proceedings of the fourth International Symposium on Imprecise Probabilities and Their Applications*. Pittsburgh, Pennsylvania, USA , Jul 20-23, 2005. SIPTA , 11-20 .## BIB

@inproceedings{antonucci2005a, address = {Pittsburgh, Pennsylvania, USA}, author = {Antonucci, Alessandro and Zaffalon, Marco}, booktitle = {ISIPTA '06: Proceedings of the fourth {I}nternational {S}ymposium on {I}mprecise {P}robabilities and {T}heir {A}pplications}, editor = {Cozman, Fabio Gagliardi and Nau, Robert and Seidenfeld, Teddy}, eventdate = {Jul 20-23, 2005}, pages = {11-20}, publisher = {SIPTA}, title = {Fast Algorithms for Robust Classification with {B}ayesian Nets}, year = {2005} }

## ABS

We focus on a well-known classification task with expert systems based on Bayesian networks: predicting the state of a target variable given an incomplete observation of the other variables in the network, i.e., an observation of a subset of all the possible variables. To provide conclusions robust to near-ignorance about the process that prevents some of the variables from being observed, it has recently been derived a new rule, called conservative updating. With this paper we address the problem to efficiently compute the conservative updating rule for robust classification with Bayesian networks. We show first that the general problem is NP-hard, thus establishing a fundamental limit to the possibility to do robust classification efficiently. Then we define a wide subclass of Bayesian networks that does admit efficient computation. We show this by developing a new classification algorithm for such a class, which extends substantially the limits of efficient computation with respect to the previously existing algorithm.

#### Hazard Assessment of Debris Flows by Credal Networks

##### Antonucci, Alessandro and Salvetti, Andrea and Zaffalon, Marco (2004).

In Pahl-Wostl, C. and Schmidt, S. and Rizzoli, A. E. and Jakeman, A. J. (Eds),

*iEMSs 2004: Complexity and Integrated Resources Management, Transactions of the 2nd Biennial Meeting of the International Environmental Modelling and Software Society*. Osnanbrück, Germany , Jun 14-17, 2004. iEMSs , 98–103 .## BIB

@inproceedings{antonucci2004a, author = {Antonucci, Alessandro and Salvetti, Andrea and Zaffalon, Marco}, booktitle = {iEMSs 2004: Complexity and Integrated Resources Management, Transactions of the 2nd Biennial Meeting of the International Environmental Modelling and Software Society}, editor = {Pahl-Wostl, C. and Schmidt, S. and Rizzoli, A. E. and Jakeman, A. J.}, eventdate = {Jun 14-17, 2004}, organization = {Manno, Switzerland}, pages = {98--103}, publisher = {iEMSs}, title = {Hazard Assessment of Debris Flows by Credal Networks}, url = {http://www.iemss.org/iemss2004/pdf/ai/antohaza.pdf}, address = {Osnanbr{\"u}ck, Germany}, year = {2004}, bdsk-url-1 = {http://www.iemss.org/iemss2004/pdf/ai/antohaza.pdf} }

## ABS

Debris flows are destructive natural hazards that affect human life, buildings, and infrastructures. Despite their importance, debris flows are only partially understood, and human expertise still plays a key role for hazard identification. This paper proposes filling the modelling gap by using credal networks, an imprecise-probability model. The model uses a directed graph to capture the causal relationships between the triggering factors of debris flows. Quantitative influences are represented by probability intervals, determined from historical data, expert knowledge, and theoretical models. Most importantly, the model joins the empirical and the quantitative modelling levels, in the direction of more credible inferences. The model is evaluated on real case studies related to dangerous areas of the Ticino Canton, southern Switzerland. The case studies highlight the good capabilities of the model: for all the areas the model produces significant probabilities of hazard.

#### Assessing Debris Flow Hazard by Credal Nets

##### Antonucci, Alessandro and Salvetti, Andrea and Zaffalon, Marco (2004).

In Lopez-Diaz, M. and Gil, M. A. and Grzegorzewski, P. and Hryniewicz, O. and Lawry, J. (Eds),

*Proceedings of the Second International Conference on Soft Methods in Probability and Statistics (SMPS-2004) - Soft Methodology and Random Information Systems*. Oviedo, Spain , Sep 2-4, 2004. Springer , 125–132 .## BIB

@inproceedings{antonucci2004b, author = {Antonucci, Alessandro and Salvetti, Andrea and Zaffalon, Marco}, booktitle = {Proceedings of the Second International Conference on {S}oft {M}ethods in {P}robability and {S}tatistics ({SMPS}-2004) - Soft Methodology and Random Information Systems}, editor = {Lopez-Diaz, M. and Gil, M. A. and Grzegorzewski, P. and Hryniewicz, O. and Lawry, J.}, eventdate = {Sep 2-4, 2004}, pages = {125--132}, publisher = {Springer}, title = {Assessing Debris Flow Hazard by Credal Nets}, url = {http://www.idsia.ch/~zaffalon/papers/smps2004.pdf}, address = {Oviedo, Spain}, year = {2004}, bdsk-url-1 = {http://www.idsia.ch/~zaffalon/papers/smps2004.pdf} }

#### Uncertain reasoning

##### Antonucci, Alessandro and Benferhat, Salem and Premaratne, Kamal (2021)

Annals of Mathematics and Artificial Intelligence, Volume 89, issue 10-11 , Springer.

## BIB

@book{antonucci2021c, editor = {Antonucci, Alessandro and Benferhat, Salem and Premaratne, Kamal}, publisher = {Springer}, title = {Uncertain reasoning}, year = {2021}, series = {Annals of Mathematics and Artificial Intelligence, Volume 89, issue 10-11}, url = {https://link.springer.com/journal/10472/volumes-and-issues/89-10} }

#### Special Issue on the Tenth International Symposium on Imprecise Probability: Theories and Applications (ISIPTA ’17)

##### Antonucci, Alessandro and Corani, Giorgio and Couso, Inés and Destercke, Sébastien (2020)

International Journal of Approximate Reasoning , Elsevier.

## BIB

@book{antonucci2018e, title = {Special Issue on the Tenth International Symposium on Imprecise Probability: Theories and Applications (ISIPTA ’17)}, editor = {Antonucci, Alessandro and Corani, Giorgio and Couso, In{\'{e}}s and Destercke, S{\'{e}}bastien}, publisher = {Elsevier}, year = {2020}, url = {https://www.sciencedirect.com/journal/international-journal-of-approximate-reasoning/special-issue/105SKX9CD05}, series = {International Journal of Approximate Reasoning} }

#### Special Issue on the Fourteenth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2017)

##### Antonucci, Alessandro and Cholvy, Laurence and Papini, Odile (2019)

International Journal of Approximate Reasoning , Elsevier.

## BIB

@book{antonucci2017c, editor = {Antonucci, Alessandro and Cholvy, Laurence and Papini, Odile}, title = {Special Issue on the Fourteenth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2017)}, publisher = {Elsevier}, year = {2019}, url = {https://www.sciencedirect.com/journal/international-journal-of-approximate-reasoning/special-issue/10ZV3BL0H39}, series = {International Journal of Approximate Reasoning} }

#### Special Issue on the Eighth Edition of the International Conference on Probabilistic Graphical Models (PGM 2016)

##### Antonucci, Alessandro and Corani, Giorgio and de Campos, Cassio Polpo (2018)

International Journal of Approximate Reasoning , Elsevier.

## BIB

@book{antonucci2018d, title = {Special Issue on the Eighth Edition of the International Conference on Probabilistic Graphical Models (PGM 2016)}, editor = {Antonucci, Alessandro and Corani, Giorgio and de Campos, Cassio Polpo}, publisher = {Elsevier}, year = {2018}, url = {https://www.sciencedirect.com/journal/international-journal-of-approximate-reasoning/special-issue/10F9CF75B8K}, series = {International Journal of Approximate Reasoning} }

#### Symbolic and Quantitative Approaches to Reasoning with Uncertainty - 14th European Conference, ECSQARU 2017, Lugano, Switzerland, July 10-14, 2017, Proceedings

##### Antonucci, Alessandro and Cholvy, Laurence and Papini, Odile (2017)

Lecture Notes in Computer Science

**10369**, Springer.## BIB

@book{antonucci2017b, editor = {Antonucci, Alessandro and Cholvy, Laurence and Papini, Odile}, title = {Symbolic and Quantitative Approaches to Reasoning with Uncertainty - 14th European Conference, {ECSQARU} 2017, Lugano, Switzerland, July 10-14, 2017, Proceedings}, series = {Lecture Notes in Computer Science}, volume = {10369}, publisher = {Springer}, year = {2017}, url = {https://doi.org/10.1007/978-3-319-61581-3}, doi = {10.1007/978-3-319-61581-3} }

#### Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, Lugano, Switzerland, 10-14 July 2017

##### Antonucci, Alessandro and Corani, Giorgio and Couso, Inés and Destercke, Sébastien (2017)

Proceedings of Machine Learning Research

**62**, PMLR.## BIB

@book{antonucci2017d, editor = {Antonucci, Alessandro and Corani, Giorgio and Couso, In{\'{e}}s and Destercke, S{\'{e}}bastien}, title = {Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, Lugano, Switzerland, 10-14 July 2017}, series = {Proceedings of Machine Learning Research}, volume = {62}, publisher = {{PMLR}}, year = {2017}, url = {http://proceedings.mlr.press/v62/} }

#### Proceedings of the Eight International Conference on Probabilistic Graphical Models, Lugano, Switzerland, 6-9 Septermber 2016

##### Antonucci, Alessandro and Corani, Giorgio and de Campos, Cassio Polpo (2016)

Proceedings of Machine Learning Research

**52**, PMLR.## BIB

@book{antonucci2016a, title = {Proceedings of the Eight International Conference on Probabilistic Graphical Models, Lugano, Switzerland, 6-9 Septermber 2016}, editor = {Antonucci, Alessandro and Corani, Giorgio and de Campos, Cassio Polpo}, publisher = {PMLR}, year = {2016}, url = {http://proceedings.mlr.press/v52}, series = {Proceedings of Machine Learning Research}, volume = {52} }