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.

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.

To date, most probabilistic reasoning systems have relied on a fixed belief network constructed at design time. The network is used by an application program as a representation of (in)dependencies in the domain. Probabilistic inference algorithms operate over the network to answer queries. Recognizing the inflexibility of fixed models has led researchers to develop automated network construction procedures that use an expressive knowledge base to generate a network that can answer a query. Although more flexible than fixed model approaches, these construction procedures separate construction and evaluation into distinct phases. In this paper we develop an approach to combining incremental construction and evaluation of a partial probability model. The combined method holds promise for improved methods for control of model construction based on a trade-off between fidelity of results and cost of construction.

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.

This article offers a modification of Chow and Liu's learning algorithm in the context of handwritten digit recognition. The modified algorithm directs the user to group digits into several classes consisting of digits that are hard to distinguish and then constructing an optimal conditional tree representation for each class of digits instead of for each single digit as done by Chow and Liu (1968). Advantages and extensions of the new method are discussed. Related works of Wong and Wang (1977) and Wong and Poon (1989) which offer a different entropy-based learning algorithm are shown to rest on inappropriate assumptions.

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.

Bayesian reinforcement learning [1], [2] is the decisiontheoretic approach [3] to solving the reinforcement learning problem. Unfonrtunately, calculating posterior distributions can be computationally expensive. Morever, the Bayesoptimal decision can be intractable [4], [5], [1], and even calculating an optimal solution in a restricted class can be difficult [6]. This paper proposes a set of algorithms that take actions by estimating bounds on the Bayes-optimal utility through sampling. They include a direct Monte-Carlo approach, as well as gradient-based approaches. We demonstrate the effectiveness of the proposed algorithms experimentally. A. Setting In the reinforcement learning problem, an agent is acting in some unknown Markovian environment µ M, according to some policy π Π. The agent's policy is a procedure for selecting actions, with the action at time t being a

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.