Most algorithms for solving POMDPs iteratively improve a value function that implicitly represents a policy and are said to search in value function space. This paper presents an approach to solving POMDPs that represents a policy explicitly as a finite-state controller and iteratively improves the controller by search in policy space. Two related algorithms illustrate this approach. The first is a policy iteration algorithm that can outperform value iteration in solving infinitehorizon POMDPs. It provides the foundation for a new heuristic search algorithm that promises further speedup by focusing computational effort on regions of the problem space that are reachable, or likely to be reached, from a start state.

While decision theory provides an appealing normative framework for representing rich preference structures, eliciting utility or value functions typically incurs a large cost. For many applications involving interactive systems this overhead precludes the use of formal decision-theoretic models of preference. Instead of performing elicitation in a vacuum, it would be useful if we could augment directly elicited preferences with some appropriate default information. In this paper we propose a case-based approach to alleviating the preference elicitation bottleneck. Assuming the existence of a population of users from whom we have elicited complete or incomplete preference structures, we propose eliciting the preferences of a new user interactively and incrementally, using the closest existing preference structures as potential defaults. Since a notion of closeness demands a measure of distance among preference structures, this paper takes the first step of studying various distance measures over fully and partially specified preference structures. We explore the use of Euclidean distance, Spearman's footrule, and define a new measure, the probabilistic distance. We provide computational techniques for all three measures.

This paper (1)shows that the best supported current psychological theory (Cheng, 1997) of how human subjects judge the causal power or influence of variations in presence or absence of one feature on another, given data on their covariation, tacitly uses a Bayes network which is either a noisy or gate (for causes that promote the effect) or a noisy and gate (for causes that inhibit the effect); (2)generalizes Chengs theory to arbitrary acyclic networks of noisy or and noisy and gates; (3)gives various sufficient conditions for the estimation of the parameters in such networks when there are independent, unobserved causes; (4)distinguishes direct causal influence of one feature on another (influence along a path with one edge) from total influence (influence along all paths from one variable to another) and gives sufficient conditions for estimating each when there are unobserved causes of the outcome variable; (5)describes the relation between Cheng models and a simplified version of the Rubin framework for representing causal relations.

Dynamic probabilistic networks are a compact representation of complex stochastic processes. In this paper we examine how to learn the structure of a DPN from data. We extend structure scoring rules for standard probabilistic networks to the dynamic case, and show how to search for structure when some of the variables are hidden. Finally, we examine two applications where such a technology might be useful: predicting and classifying dynamic behaviors, and learning causal orderings in biological processes. We provide empirical results that demonstrate the applicability of our methods in both domains.

In recent years there has been a flurry of works on learning Bayesian networks from data. One of the hard problems in this area is how to effectively learn the structure of a belief network from incomplete data- that is, in the presence of missing values or hidden variables. In a recent paper, I introduced an algorithm called Structural EM that combines the standard Expectation Maximization (EM) algorithm, which optimizes parameters, with structure search for model selection. That algorithm learns networks based on penalized likelihood scores, which include the BIC/MDL score and various approximations to the Bayesian score. In this paper, I extend Structural EM to deal directly with Bayesian model selection. I prove the convergence of the resulting algorithm and show how to apply it for learning a large class of probabilistic models, including Bayesian networks and some variants thereof.

This paper presents an axiomatic framework for qualitative decision under uncertainty in a finite setting. The corresponding utility is expressed by a sup-min expression, called Sugeno (or fuzzy) integral. Technically speaking, Sugeno integral is a median, which is indeed a qualitative counterpart to the averaging operation underlying expected utility. The axiomatic justification of Sugeno integral-based utility is expressed in terms of preference between acts as in Savage decision theory. Pessimistic and optimistic qualitative utilities, based on necessity and possibility measures, previously introduced by two of the authors, can be retrieved in this setting by adding appropriate axioms.

This paper relates comparative belief structures and a general view of belief management in the setting of deductively closed logical representations of accepted beliefs. We show that the range of compatibility between the classical deductive closure and uncertain reasoning covers precisely the nonmonotonic 'preferential' inference system of Kraus, Lehmann and Magidor and nothing else. In terms of uncertain reasoning any possibility or necessity measure gives birth to a structure of accepted beliefs. The classes of probability functions and of Shafer's belief functions which yield belief sets prove to be very special ones.

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.

It is well known that one can ignore parts of a belief network when computing answers to certain probabilistic queries. It is also well known that the ignorable parts (if any) depend on the specific query of interest and, therefore, may change as the query changes. Algorithms based on jointrees, however, do not seem to take computational advantage of these facts given that they typically construct jointrees for worst-case queries; that is, queries for which every part of the belief network is considered relevant. To address this limitation, we propose in this paper a method for reconfiguring jointrees dynamically as the query changes. The reconfiguration process aims at maintaining a jointree which corresponds to the underlying belief network after it has been pruned given the current query. Our reconfiguration method is marked by three characteristics: (a) it is based on a non-classical definition of jointrees; (b) it is relatively efficient; and (c) it can reuse some of the computations performed before a jointree is reconfigured. We present preliminary experimental results which demonstrate significant savings over using static jointrees when query changes are considerable.

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.