Though the Bayesian network is one of methods for probabilistic inferences in the artificial intelligence, also probabilistic models in the image processing based on the Bayesian statistics are regarded as Bayesian networks[1, 2, 3]. As one of approximate algorithms for probabilistic inferences by using Bayesian networks, belief propagation has been investigated[4, 5, 6, 7]. Recently, the belie...

Graphical models, such as Bayesian networks and Markov random elds represent statistical dependencies of variables by a graph. Local \belief propagation" rules of the sort proposed by Pearl [20] are guaranteed to converge to the correct posterior probabilities in singly connected graphs. Recently good performance has been obtained by using these same rules on graphs with loops, a method known a...

The complexity of the exact inference increases exponentially with size and complexity of the network. As a result, the exact inference methods become impractical for large networks and we seek to approximate the results. A variety of approximation methods exist. This research focuses on two approximation methods for finding posterior marginals P (xi|e) in Bayesian networks: iterative belief up...

Een wetenschappelijke proeve op het gebied van de Natuurwetenschappen, Wiskunde en Informatica Proefschrift ter verkrijging van de graad van doctor aan de Radboud Universiteit Nijmegen, op gezag van de rector magnificus prof. mr. Contents Title page i Table of Contents iii 1 Introduction 1 1.1 A gentle introduction to graphical models 1 1.1.1 The Asia network: an example of a Bayesian network 2...

We have created a logic-based, first-order, and Turingcomplete set of software tools for stochastic modeling. Because the inference scheme for this language is based on a variant of Pearl's loopy belief propagation algorithm, we call it Loopy Logic. Traditional Bayesian belief networks have limited expressive power, basically constrained to that of atomic elements as in the propositional calcul...

Bayesian (also called Belief) Networks (BN) are a powerful knowledge representation and reasoning mechanism. BN represent events and causal relationships between them as conditional probabilities involving random variables. Given the values of a subset of these variables (evidence variables) BN can compute the probabilities of another subset of variables (query variables). BN can be created aut...

Bayesian networks are gaining an increasing popularity as a modeling tool for complex problems involving reasoning under uncertainty. Since belief updating in very large Bayesian networks cannot be effectively addressed by exact methods, approximate inference schemes may be often the only computationally feasible alternative. There are two basic classes of approximate schemes: stochastic sampli...

SUMMARY This paper addresses the problem of learning Bayesian belief networks (BBN) based on the minimum description length (MDL) principle. First, we give a formula of description length based on which the MDL-based procedure learns a BBN. Secondly, we point out that the difference between the MDL-based and Cooper and Herskovits procedures is essentially in the priors rather than in the approa...

Monte Carlo sampling has become a major vehicle for approximate inference in Bayesian networks. In this paper, we investigate a fam­ ily of related simulation approaches, known collectively as quasi-Monte Carlo methods based on deterministic low-discrepancy se­ quences. We first outline several theoreti­ cal aspects of deterministic low-discrepancy sequences, show three examples of such se­ que...