Sensitivity Analysis in Graphical Models with Imprecise Probabilities: Applications to Robust Data Mining and Decision Support Systems (T22)

Abstract

Probabilistic graphical models such as Bayesian networks or Markov random fields need a sharp estimate of their parameters: such a precise elicitation might be unreliable because of limited expert knowledge or few/incomplete data to learn from. During this tutorial we present a number of optimization techniques, based on the theory of imprecise probability, to analyze the sensitivity of the inferences in graphical models with respect to perturbations in the parameters; applications to single- and multi-dimensional classification, computer vision, and decision support in knowledge-based expert systems are also provided.

Outline and Material

• Part 0: Basics about graphical models and sensitivity analysis


• Bayesian networks (BNs)
• Existing approaches to sensitivity analysis in BNs
• The imprecise probability approach to SA


• Part 1: SA of inferences in BNs by Cassio P. de Campos (slides, R code)


• Robust BNs
• SA of updating in BNs
• SA of MAP inference in BNs


• Part 2: SA of classifiers based on BNs by Alessandro Antonucci (slides)


• Standard classification (robust naive Bayes)
• Robust multi-label classification
• SA of time series classification (based on HMMs)
• Performance evaluation

The Speakers

Cassio Polpo de Campos is a Reader with Queen’s University Belfast, UK. He obtained his PhD in 2006 with a thesis about algorithms and computational complexity in Bayesian and credal networks and his Habilitation in 2013 related to the same topics, both from the University of Sao Paulo, Brazil. Author of more than 70 publications in probabilistic graphical models, imprecise probability, computational complexity and bioinformatics. He serves as program committee member of prestigious conferences in machine learning and artificial intelligence, and is currently an at-large member in the executive committee of the Society for Imprecise Probability.

Alessandro Antonucci is a Senior Researcher at IDSIA (Switzerland). He teaches at the University of Applied Sciences and Arts of Southern Switzerland. He is the author of about 50 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 the Swiss Army.