Learning Possibilistic Networks from Data

We introduce a method for inducing the structure of (causal) possibilistic networks from databases of sample cases. In comparison to the construction of Bayesian belief networks, the proposed framework has some advantages, namely the explicit consideration of imprecise (set-valued) data, and the realization of a controlled form of information compression in order to increase the eeciency of the learning strategy as well as approximate reasoning using local propagation techniques. Our learning method has been applied to reconstruct a non-singly connected network of 22 nodes and 24 arcs without the need of any a priori supplied node ordering. 14.1 Introduction Bayesian networks provide a well-founded normative framework for knowledge representation and reasoning with uncertain, but precise data. Extending pure probabilistic settings to the treatment of imprecise (set-valued) information usually restricts the computational tractability of the corresponding inference mechanisms. It is therefore near at hand to consider alternative uncertainty calculi that provide a justiied form of information compression in order to support eecient reasoning in the presence of imprecise and uncertain data without aaecting the expressive power and correctness of decision making. Such a modelling approach is appropriate for systems that accept approximate instead of crisp reasoning due to a non-signiicant sensitivity concerning slight changes of information. Possibility theory Zadeh78, Dubois88] seems to be a promising framework for this purpose. In this paper we focus our interest on the concept of a possibilistic causal network, which is a directed acyclic graph (DAG) and a family of (conditional) possibility distributions. Since the covering of all aspects of possibilistic reasoning is beyond the scope of this paper, we will connne to the problem of inducing the structure of a possibilistic causal network from data. In Section 14.2 we introduce a possibilistic interpretation of databases of set-valued samples. Based on this semantic background, Sections 14.3 and 14.4 deal with possibilistic networks and the structure induction method, respectively. In Section 14.5, we mention some basic ideas and important results including an example of the successful application of our approach.