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Unifying graphical models by credal networks: algorithms and applications

People

 

Zaffalon M.

(Responsible)

Abstract

We consider the problem of learning models and doing predictions in presence of incomplete information. Examples of incomplete information are incomplete data sets and, more generally, incomplete information on the basis of which we have to take a decision. The great majority of the approaches to incompleteness in the scientific literature regards it as uninformative. This means that incompleteness is intended to happen following "random" patterns, and the goal of the analysis is just to filter it out in order to recover the underlying "signal". Nowadays, there is some criticism about these approaches as they often lead to fragile models and (sometimes highly) misleading conclusions. The point is that regarding incompleteness as uninformative is often too a narrow view.































































Our past work has instead shown that it is actually possible to work with more general views of incompleteness, by introducing a so-called conservative updating rule. This rule prescribes, in the framework of expert systems, how to update beliefs under incomplete information when there is nearly no knowledge about the process that gives rise to the incompleteness. In this project we will generalize such a work in two directions: to more complex states of knowledge about the incompleteness process, and to the statistical case, thus deriving new types of conservative rules.































































At the algorithmic level, the goal of this project will be to make the new conservative rules practical for use with real-world problems. For this part, we will mostly focus on Bayesian and credal networks. Bayesian nets are probabilistic graphical models; credal networks generalize Bayesian networks to sets of probability distributions. This part of the project will develop generalized versions of Bayesian and credal networks that implement the derived conservative rules for incomplete information. In particular we plan to develop the following tasks:- To make a previous algorithm of ours for expert systems fully consistent with the new conservative rules, and apt to deal with general networks.- Since we believe that there is a natural connection between Bayesian networks that implement the new rules and credal networks that implement the traditional conditioning, we plan to show precisely how the two models are connected in order to provide a general way to transform the former into the latter and vice versa.- In the same spirit of the last point, we plan to make the existing L2U algorithm for credal networks fully general. This is a cutting-edge algorithm to solve inferential tasks on credal networks. Its drawback is dealing only with binary random variables. We plan to extend it to general variables by transforming a general network to a network with binary variables to which the current version of L2U can apply.

Additional information

Start date
01.03.2008
End date
01.04.2011
Duration
37 Months
Funding sources
SNSF
Status
Ended
Category
Swiss National Science Foundation / Project Funding / Mathematics, Natural and Engineering Sciences (Division II)