Bayesian networks with imprecise probabilities: theory and applications to knowledge-based systems and classification

by Alessandro Antonucci, Giorgio Corani, Denis Maua'

A tutorial presented at IJCAI 2013 (23rd International Joint Conference on Artificial Intelligence)

Monday, August 5th, 2013 (9.00 - 12.45)- Beijing International Convention Center, Beijing (China)

Abstract

Bayesian networks are important tools for uncertain reasoning in AI; their quantification requires a precise assessment of the conditional probabilities. Credal networks generalize Bayesian networks, so that probabilities can vary in a set (e.g., interval). This provides a more realistic model of expert knowledge and returns more robust inferences. The first part of this tutorial describes the specification procedure for credal network, the existing inference algorithms and approaches to decision making; two prototypical examples of knowledge-based expert systems related to military decision making and environmental risk analysis based on credal networks are indeed presented. In the second part, we describe the major examples of credal classifiers, i.e., classification algorithms based on credal networks, developed so far. Credal classifiers generalize the traditional Bayesian classifiers, which are based on a single prior density and on a single likelihood. Credal classifiers are instead based on (i) a set of priors, thus removing the need for subjectively choosing a prior and (ii) possibly also on a set of likelihoods, to allow robust classification even with missing data. Credal classifiers can return more classes if the assignment to a single class is too uncertain; in this way, they preserve reliability. The tutorial presents algorithms for credal classification and comparison with traditional classifiers on a large number of data sets. Also the problem of evaluating performance of a classifier possibly returning multiple output and alternative quantification techniques are discussed.

Material

The tutorialists

Alessandro Antonucci is a researcher at IDSIA (Switzerland). He teaches at the University of Applied Sciences and Arts of Southern Switzerland (SUPSI). He is the author of about 40 publications, mostly in the area of probabilistic graphical models with imprecise probability. He is currently working on a number of projects for the application of imprecise probabilistic graphical models to the development of knowledge-based systems and classifiers. In particular, he is developing a credal network for military decision making for Armasuisse. He was also the Executive Editor and the treasurer of the Society for Imprecise Probability: Theories and Applications (SIPTA). More information here.

Giorgio Corani is a researcher at IDSIA (Switzerland). He is author of about 50 publications in the area of probabilistic graphical models with imprecise probabilities (credal classifiers), data mining and applied statistics. He is in the program committee of ISIPTA (International Symposium on Imprecise Probabilities and Their Applications). He teaches 'Uncertain Reasoning and Data Mining' and 'Applied Statistics' at the University of Lugano (Switzerland). More information here.

Denis Maua is a Ph.D. candidate at University of Lugano (USI), and a researcher at IDSIA. His work is focused on probabilistic graphical models and their applications. More information here.