Bayesiannetworks provide a languagefor qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms.

. We examine a novel addition to the known methods for learning Bayesian networks from data that improves the quality of the learned networks. Our approach explicitly represents and learns the local structure in the conditional probability distributions (CPDs) that quantify these networks. This increases the space of possible models, enabling the representation of CPDs with a variable number of parameters. The resulting learning procedure induces models that better emulate the interactions present in the data. We describe the theoretical foundations and practical aspects of learning local structures and provide an empirical evaluation of the proposed learning procedure. This evaluation indicates that learning curves characterizing this procedure converge faster, in the number of training instances, than those of the standard procedure, which ignores the local structure of the CPDs. Our results also show that networks learned with local structures tend to be more complex (in terms of a...

A new method is proposed for exploiting causal independencies in exact Bayesian network inference.

Stochastic sampling algorithms, while an attractive alternative to exact algorithms in very large Bayesian network models, have been observed to perform poorly in evidential reasoning with extremely unlikely evidence. To address this problem, we propose an adaptive importance sampling algorithm, AIS-BN, that shows promising convergence rates even under extreme conditions and seems to outperform the existing sampling algorithms consistently. Three sources of this performance improvement are (1) two heuristics for initialization of the importance function that are based on the theoretical properties of importance sampling in nite-dimensional integrals and the structural advantages of Bayesian networks, (2) a smooth learning method for the importance function, and (3) a dynamic weighting function for combining samples from dierent stages of the algorithm. We tested the performance of the AIS-BN algorithm along with two state of the art general purpose sampling algorithms, lik...

ABayesian network is a probabilistic representation for uncertain relationships, which has proven to be useful for modeling real-world problems. When there are many potential causes of a given e ect, however, both probability assessment and inference using a Bayesian network can be di cult. In this paper, we describe causal independence, a collection of conditional independence assertions and functional relationships that are often appropriate to apply to the representation of the uncertain interactions between causes and e ect. We show how the use of causal independence in a Bayesian network can greatly simplify probability assessment aswell as probabilistic inference. 1

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The paper presents a class of approximation algorithms that extend the idea of bounded inference, inspired by successful constraint propagation algorithms, to probabilistic inference and combinatorial optimization. The idea is to bound the dimensionality of dependencies created by inference algorithms. This yields a parameterized scheme, called mini-buckets, that offers adjustable levels of accuracy and efficiency. The mini-bucket approach generates both an approximate solution and a bound on the solution quality. We present empirical results demonstrating successful performance of the proposed approximation scheme for probabilistic tasks, both on randomly generated problems and on realistic domains such as medical diagnosis and probabilistic decoding. 1 Introduction Automated reasoning tasks such as constraint satisfaction and optimization, probabilistic inference, decision-making, and planning are generally hard (NP-hard). One way to cope This work was partially supported...

We develop a series of approximations for decision-theoretic troubleshooting under uncertainty. Our approach generates troubleshooting plans in the face of uncertainty in the relationships among components and device status, observations, as well as the affect of actions on device status. Included in our approach is a Bayesian-network representation of these relationships. We have applied our technique successfully to troubleshooting problems with printing, photocopier feeders, automobiles, and gas turbines. We report empirical findings demonstrating the high quality of plans produced by our approach. 1

Bayesian belief networks have grown to prominence because they provide compact representations of many domains, and there are algorithms to exploit this compactness. The next step is to allow compact representations of the conditional probability tables of a variable given its parents. In this paper we present such a representation in terms of parent contexts and provide an algorithm that exploits this compactness. The representation is in terms of rules that provide conditional probabilities in different contexts. The algorithm is based on eliminating the variables not needed in an answer in turn. The operations for eliminating a variable correspond to a form of partial evaluation, where we are careful to maintain the probabilistic dependencies necessary for correct probabilistic inference. We show how this new method can exploit more structure than previous methods for structured belief network inference. 1

A probabilistic network is a graphical model that encodes probabilistic relationships between variables of interest. Such a model records qualitative influences between variables in addition to the numerical parameters of the probability distribution. As such it provides an ideal form for combining prior knowledge, which might be limited solely to experience of the influences between some of the variables of interest, and data. In this paper, we first show how data can be used to revise initial estimates of the parameters of a model. We then progress to showing how the structure of the model can be revised as data is obtained. Techniques for learning with incomplete data are also covered.