In this paper we address the problem of discretization in the context of learning Bayesian networks (BNs) from data containing both continuous and discrete variables. We describe a new technique for multivariate discretization, whereby each continuous variable is discretized while taking into account its interaction with the other variables. The technique is based on the use of a Bayesian scoring metric that scores the discretization policy for a continuous variable given a BN structure and the observed data. Since the metric is relative to the BN structure currently being evaluated, the discretization of a variable needs to be dynamically adjusted as the BN structure changes.

We exploit qualitative probabilistic relationships among variables for computing bounds of conditional probability distributions of interest in Bayesian networks. Using the signs of qualitative relationships, we can implement abstraction operations that are guaranteed to bound the distributions of interest in the desired direction. By evaluating incrementally improved approximate networks, our algorithm obtains monotonically tightening bounds that converge to exact distributions. For supermodular utility functions, the tightening bounds monotonically reduce the set of admissible decision alternatives as well.

The variability of structure in a finite Markov equivalence class of causally sufficient models represented by directed acyclic graphs has been fully characterized. Without causal sufficiency, an infinite semi-Markov equivalence class of models has only been characterized by the fact that each model in the equivalence class entails the same marginal statistical dependencies. In this paper, we study the variability of structure of causal models within a semi-Markov equivalence class and propose a systematic approach to construct models entailing any specific marginal statistical dependencies.

There exist two general forms of exact algorithms for updating probabilities in Bayesian Networks. The first approach involves using a structure, usually a clique tree, and performing local message based calculation to extract the belief in each variable. The second general class of algorithm involves the use of non-serial dynamic programming techniques to extract the belief in some desired group of variables. In this paper we present a hybrid algorithm based on the latter approach yet possessing the ability to retrieve the belief in all single variables. The technique is advantageous in that it saves a NP-hard computation step over using one algorithm of each type. Furthermore, this technique re-enforces a conjecture of Jensen and Jensen [JJ94] in that it still requires a single NP-hard step to set up the structure on which inference is performed, as we show by confirming Li and D'Ambrosio's [LD94] conjectured NP-hardness of OFP.

In the last decade, several architectures have been proposed for exact computation of marginals using local computation. In this paper, we compare three architectures - Lauritzen-Spiegelhalter, Hugin, and Shenoy-Shafer - from the perspective of graphical structure for message propagation, message-passing scheme, computational efficiency, and storage efficiency.

We present an anytime algorithm which computes policies for decision problems represented as multi-stage influence diagrams. Our algorithm constructs policies incrementally, starting from a policy which makes no use of the available information. The incremental process constructs policies which includes more of the information available to the decision maker at each step. While the process converges to the optimal policy, our approach is designed for situations in which computing the optimal policy is infeasible. We provide examples of the process on several large decision problems, showing that, for these examples, the process constructs valuable (but sub-optimal) policies before the optimal policy would be available by traditional methods.

This paper analyzes irrelevance and independence relations in graphical models associated with convex sets of probability distributions (called Quasi-Bayesian networks). The basic question in Quasi-Bayesian networks is, How can irrelevance/independence relations in Quasi-Bayesian networks be detected, enforced and exploited? This paper addresses these questions through Walley's definitions of irrelevance and independence. Novel algorithms and results are presented for inferences with the so-called natural extensions using fractional linear programming, and the properties of the so-called type-1 extensions are clarified through a new generalization of d-separation.

This paper is about reducing influence diagram (ID) evaluation into Bayesian network (BN) inference problems. Such reduction is interesting because it enables one to readily use one's favorite BN inference algorithm to efficiently evaluate IDs. Two such reduction methods have been proposed previously (Cooper 1988, Shachter and Peot 1992). This paper proposes a new method. The BN inference problems induced by the mew method are much easier to solve than those induced by the two previous methods.

This paper describes a decision theoretic formulation of learning the graphical structure of a Bayesian Belief Network from data. This framework subsumes the standard Bayesian approach of choosing the model with the largest posterior probability as the solution of a decision problem with a 0-1 loss function and allows the use of more general loss functions able to trade-off the complexity of the selected model and the error of choosing an oversimplified model. A new class of loss functions, called disintegrable, is introduced, to allow the decision problem to match the decomposability of the graphical model. With this class of loss functions, the optimal solution to the decision problem can be found using an efficient bottom-up search strategy.

We take another look at the general problem of selecting a preferred probability measure among those that comply with some given constraints. The dominant role that entropy maximization has obtained in this context is questioned by arguing that the minimum information principle on which it is based could be supplanted by an at least as plausible "likelihood of evidence" principle. We then review a method for turning given selection functions into representation independent variants, and discuss the tradeoffs involved in this transformation.