Bayesian networks are directed acyclic graphs representing independence relationships among a set of random variables. A random variable can be regarded as a set of exhaustive and mutually exclusive propositions. We argue that there are several drawbacks resulting from the propositional nature and acyclic structure of Bayesian networks. To remedy these shortcomings, we propose a probabilistic network where nodes represent unary predicates and which may contain directed cycles. The proposed representation allows us to represent domain knowledge in a single static network even though we cannot determine the instantiations of the predicates before hand. The ability to deal with cycles also enables us to handle cyclic causal tendencies and to recognize recursive plans.

This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across repeated problem instances. Asymptotic methods are used to derive an approximate distribution for the test statistic. When the model is rejected, the individual components of the test statistic can be used to guide search for an alternate model.

The leading contender is Levi's When the set contains only one function, convex conditionalization and E-admissibility reduce to their strict Bayesian counterparts. Thus, with respect to decision making and representing and updating uncertainty, convex Bay· esianism includes strict Bayesianism as a special case. There are natural constraints on probability judg-- ments that cannot be represented by convex sets of classical probability functions. Working with the convex hull of a nonconvex set of probability func-- tions may result in unnecessary indecisiveness. This is not a convex set. Judgments of irrelevance (conditional irrelevance), that is, probabilistic independence (conditional independence}, are often made, are natural to make, can be made reliably, and provide well-known computational advantages [Pearl, 1988].

We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude of disbelief, which impose constraints over possible rankings of worlds. It was shown that, once we compute a priority function Z+ on the rules, the degree to which a given query is confirmed or denied can be computed in O(log n`) propositional satisfiability tests, where n is the number of rules in the knowledge base. In this paper, we show that computing Z+ requires O(n2 X log n) satisfiability tests, not an exponential number as was conjectured in [18], which reduces to polynomial complexity in the case of Horn expressions. We also show how reasoning with imprecise observations can be incorporated in our formalism and how the popular notions of belief revision and epistemic entrenchment are embodied naturally and tractably.

In the probabilistic approach to uncertainty management the input knowledge is usually represented by means of some probability distributions. In this paper we assume that the input knowledge is given by two discrete conditional probability distributions, represented by two stochastic matrices P and Q. The consistency of the knowledge base is analyzed. Coherence conditions and explicit formulas for the extension to marginal distributions are obtained in some special cases.

We describe how we selectively reformulate portions of a belief network that pose difficulties for solution with a stochastic-simulation algorithm. With employ the selective conditioning approach to target specific nodes in a belief network for decomposition, based on the contribution the nodes make to the tractability of stochastic simulation. We review previous work on BNRAS algorithms- randomized approximation algorithms for probabilistic inference. We show how selective conditioning can be employed to reformulate a single BNRAS problem into multiple tractable BNRAS simulation problems. We discuss how we can use another simulation algorithm-logic sampling-to solve a component of the inference problem that provides a means for knitting the solutions of individual subproblems into a final result. Finally, we analyze tradeoffs among the computational subtasks associated with the selective conditioning approach to reformulation.

Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and structural observability theorems are developed and algorithms are formulated. Controllability and observability are fundamental concepts in dynamic systems (Luenberger 1979). Controllability corresponds to the ability to control a system while observability analyzes the inferability of its variables. Both properties can be determined by the ranks of the system matrices. Structural controllability and observability, on the other hand, analyze the property of a system with its structure only, without the specific knowledge of the values of its elements (tin 1974, Shields and Pearson 1976). The structural analysis explores the connection between the structure of a model and the functional dependence among its elements. It is useful in comprehending problem and formulating solution by challenging the underlying intuitions and detecting inconsistency in a model. This type of qualitative reasoning can sometimes provide insight even when there is insufficient numerical information in a model.

Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization algorithm. When the model is conditionally conjugate, the coordinate updates are easily derived and in closed form. However, many models of interest---like the correlated topic model and Bayesian logistic regression---are nonconjuate. In these models, mean-field methods cannot be directly applied and practitioners have had to develop variational algorithms on a case-by-case basis. In this paper, we develop two generic methods for nonconjugate models, Laplace variational inference and delta method variational inference. Our methods have several advantages: they allow for easily derived variational algorithms with a wide class of nonconjugate models; they extend and unify some of the existing algorithms that have been derived for specific models; and they work well on real-world datasets. We studied our methods on the correlated topic model, Bayesian logistic regression, and hierarchical Bayesian logistic regression.

This paper describes a normative system design that incorporates diagnosis, dynamic evolution, decision making, and information gathering. A single influence diagram demonstrates the design's coherence, yet each activity is more effectively modeled and evaluated separately. Application to offshore oil platforms illustrates the design. For this application, the normative system is embedded in a real-time expert system.

In previous work we developed a method of learning Bayesian Network models from raw data. This method relies on the well known minimal description length (MDL) principle. The MDL principle is particularly well suited to this task as it allows us to tradeoff, in a principled way, the accuracy of the learned network against its practical usefulness. In this paper we present some new results that have arisen from our work. In particular, we present a new local way of computing the description length. This allows us to make significant improvements in our search algorithm. In addition, we modify our algorithm so that it can take into account partial domain information that might be provided by a domain expert. The local computation of description length also opens the door for local refinement of an existent network. The feasibility of our approach is demonstrated by experiments involving networks of a practical size.