Imprecise Probabilistic Graphical Models: Equivalent Representations, Inference Algorithms And Applications
Decanato - Facoltà di scienze informatiche
Data d'inizio: 16 Aprile 2008
Data di fine: 17 Aprile 2008
Mr. Alessandro Antonucci, Wednesday 16 April 2008 at 10:30, Auditorium
The Defense Committee:
- Dr. Marco Zaffalon, IDSIA, Switzerland (research advisor)
- Prof. Gert de Cooman, Ghent University, Belgium (external member)
- Prof. Serafín Moral, University of Granada, Spain (external member)
- Prof. Fabio Crestani, USI Università della Svizzera italiana, Switzerland (internal member)
- Prof. Luca Maria Gambardella, IDSIA, Switzerland (internal member)
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.
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 said decision-theoretic being inspired by the formalism of decision graphs, for a unified representation of credal networks of any kind. I also provide 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.
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 a special class of credal networks can be generalized to any model. I also present a state-of-the-art updating algorithm based on the equivalent binary representation. 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 are presented. First, I consider a military identification problem, consisting in the detection of the goal of an intruder entering a no-fly area. This problem is mapped by our techniques into a credal network updating task.
The second application is an environmental model for hazard assessment of debris flows. A credal network evaluates the level of risk, corresponding to the observed values of the triggering factors for this specific natural hazard.