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109
Approximating probabilistic inference in Bayesian belief networks is NPhard
, 1991
"... Abstract A belief network comprises a graphical representation of dependencies between variables of a domain and a set of conditional probabilities associated with each dependency. Unless P=NP, an efficient, exact algorithm does not exist to compute probabilistic inference in belief networks. Stoch ..."
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Cited by 287 (3 self)
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Abstract A belief network comprises a graphical representation of dependencies between variables of a domain and a set of conditional probabilities associated with each dependency. Unless P=NP, an efficient, exact algorithm does not exist to compute probabilistic inference in belief networks. Stochastic simulation methods, which often improve run times, provide an alternative to exact inference algorithms. We present such a stochastic simulation algorithm 2)BNRAS that is a randomized approximation scheme. To analyze the run time, we parameterize belief networks by the dependence value PE, which is a measure of the cumulative strengths of the belief network dependencies given background evidence E. This parameterization defines the class of fdependence networks. The run time of 2)BNRAS is polynomial when f is a polynomial function. Thus, the results of this paper prove the existence of a class of belief networks for which inference approximation is polynomial and, hence, provably faster than any exact algorithm. I.
Learning Bayesian belief networks: An approach based on the MDL principle
 Computational Intelligence
, 1994
"... A new approach for learning Bayesian belief networks from raw data is presented. The approach is based on Rissanen's Minimal Description Length (MDL) principle, which is particularly well suited for this task. Our approach does not require any prior assumptions about the distribution being lear ..."
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Cited by 247 (7 self)
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A new approach for learning Bayesian belief networks from raw data is presented. The approach is based on Rissanen's Minimal Description Length (MDL) principle, which is particularly well suited for this task. Our approach does not require any prior assumptions about the distribution being learned. In particular, our method can learn unrestricted multiplyconnected belief networks. Furthermore, unlike other approaches our method allows us to tradeo accuracy and complexity in the learned model. This is important since if the learned model is very complex (highly connected) it can be conceptually and computationally intractable. In such a case it would be preferable to use a simpler model even if it is less accurate. The MDL principle o ers a reasoned method for making this tradeo. We also show that our method generalizes previous approaches based on Kullback crossentropy. Experiments have been conducted to demonstrate the feasibility of the approach. Keywords: Knowledge Acquisition � Bayes Nets � Uncertainty Reasoning. 1
Reasoning about beliefs and actions under computational resource constraints
 in Proceedings of the 1989 Workshop on Uncertainty and AI
, 1987
"... Although many investigators arm a desire to build reasoning systems that behave consistently with the axiomatic basis dened by probability theory and utility theory, limited resources for engineering and computation can make a complete normative analysis impossible. We attempt to move discussion be ..."
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Cited by 216 (21 self)
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Although many investigators arm a desire to build reasoning systems that behave consistently with the axiomatic basis dened by probability theory and utility theory, limited resources for engineering and computation can make a complete normative analysis impossible. We attempt to move discussion beyond the debate over the scope of problems that can be handled eectively to cases where it is clear that there are insucient computational resources to perform an analysis deemed as complete. Under these conditions, we stress the importance of considering the expected costs and benets of applying alternative approximation procedures and heuristics for computation and knowledge acquisition. We discuss how knowledge about the structure of user utility can be used to control value tradeos for tailoring inference to alternative contexts. We address the notion of realtime rationality, focusing on the application of knowledge about the expected timewiserenement abilities of reasoning strategies to balance the bene ts of additional computation with the costs of acting with a partial result. We discuss the benets of applying decision theory to control the solution of dicult problems given limitations and uncertainty in reasoning resources. 1
Policy Recognition in the Abstract Hidden Markov Model
 Journal of Artificial Intelligence Research
, 2002
"... In this paper, we present a method for recognising an agent's behaviour in dynamic, noisy, uncertain domains, and across multiple levels of abstraction. We term this problem online plan recognition under uncertainty and view it generally as probabilistic inference on the stochastic process rep ..."
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Cited by 161 (25 self)
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In this paper, we present a method for recognising an agent's behaviour in dynamic, noisy, uncertain domains, and across multiple levels of abstraction. We term this problem online plan recognition under uncertainty and view it generally as probabilistic inference on the stochastic process representing the execution of the agent's plan. Our contributions in this paper are twofold. In terms of probabilistic inference, we introduce the Abstract Hidden Markov Model (AHMM), a novel type of stochastic processes, provide its dynamic Bayesian network (DBN) structure and analyse the properties of this network. We then describe an application of the RaoBlackwellised Particle Filter to the AHMM which allows us to construct an ecient, hybrid inference method for this model. In terms of plan recognition, we propose a novel plan recognition framework based on the AHMM as the plan execution model. The RaoBlackwellised hybrid inference for AHMM can take advantage of the independence properties inherent in a model of plan execution, leading to an algorithm for online probabilistic plan recognition that scales well with the number of levels in the plan hierarchy. This illustrates that while stochastic models for plan execution can be complex, they exhibit special structures which, if exploited, can lead to efficient plan recognition algorithms. We demonstrate the usefulness of the AHMM framework via a behaviour recognition system in a complex spatial environment using distributed video surveillance data.
Probabilistic Diagnosis Using a Reformulation of the INTERNIST1/QMR Knowledge Base  II. Evaluation of Diagnostic Performance
 Medicine
, 1990
"... We have developed a probabilistic reformulation of the Quick Medical Reference (QMR) system. In Part I of this twopart series, we described a twolevel, multiply connected beliefnetwork representation of the QMR knowledge base and a simulation algorithm to perform probabilistic inference on the re ..."
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Cited by 132 (11 self)
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We have developed a probabilistic reformulation of the Quick Medical Reference (QMR) system. In Part I of this twopart series, we described a twolevel, multiply connected beliefnetwork representation of the QMR knowledge base and a simulation algorithm to perform probabilistic inference on the reformulated knowledge base. In Part II of this series, we report on an evaluation of the probabilistic QMR, in which we compare the performance of QMR to that of our probabilistic system on cases abstracted from continuing medical education materials from Scientific American Medicine. In addition, we analyze empirically several components of the probabilistic model and simulation algorithm.
Decision Theory in Expert Systems and Artificial Intelligence
 International Journal of Approximate Reasoning
, 1988
"... Despite their different perspectives, artificial intelligence (AI) and the disciplines of decision science have common roots and strive for similar goals. This paper surveys the potential for addressing problems in representation, inference, knowledge engineering, and explanation within the decision ..."
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Cited by 104 (19 self)
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Despite their different perspectives, artificial intelligence (AI) and the disciplines of decision science have common roots and strive for similar goals. This paper surveys the potential for addressing problems in representation, inference, knowledge engineering, and explanation within the decisiontheoretic framework. Recent analyses of the restrictions of several traditional AI reasoning techniques, coupled with the development of more tractable and expressive decisiontheoretic representation and inference strategies, have stimulated renewed interest in decision theory and decision analysis. We describe early experience with simple probabilistic schemes for automated reasoning, review the dominant expertsystem paradigm, and survey some recent research at the crossroads of AI and decision science. In particular, we present the belief network and influence diagram representations. Finally, we discuss issues that have not been studied in detail within the expertsystems sett...
AISBN: An Adaptive Importance Sampling Algorithm for Evidential Reasoning in Large Bayesian Networks
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2000
"... 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, ..."
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Cited by 86 (3 self)
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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, AISBN, 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 nitedimensional 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 AISBN algorithm along with two state of the art general purpose sampling algorithms, lik...
An Optimal Approximation Algorithm For Bayesian Inference
 Artificial Intelligence
, 1997
"... Approximating the inference probability Pr[X = xjE = e] in any sense, even for a single evidence node E, is NPhard. This result holds for belief networks that are allowed to contain extreme conditional probabilitiesthat is, conditional probabilities arbitrarily close to 0. Nevertheless, all p ..."
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Cited by 54 (2 self)
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Approximating the inference probability Pr[X = xjE = e] in any sense, even for a single evidence node E, is NPhard. This result holds for belief networks that are allowed to contain extreme conditional probabilitiesthat is, conditional probabilities arbitrarily close to 0. Nevertheless, all previous approximation algorithms have failed to approximate efficiently many inferences, even for belief networks without extreme conditional probabilities. We prove that we can approximate efficiently probabilistic inference in belief networks without extreme conditional probabilities. We construct a randomized approximation algorithmthe boundedvariance algorithmthat is a variant of the known likelihoodweighting algorithm. The boundedvariance algorithm is the first algorithm with provably fast inference approximation on all belief networks without extreme conditional probabilities. From the boundedvariance algorithm, we construct a deterministic approximation algorithm u...
A Survey of Algorithms for RealTime Bayesian Network Inference
 In In the joint AAAI02/KDD02/UAI02 workshop on RealTime Decision Support and Diagnosis Systems
, 2002
"... As Bayesian networks are applied to more complex and realistic realworld applications, the development of more efficient inference algorithms working under realtime constraints is becoming more and more important. This paper presents a survey of various exact and approximate Bayesian network ..."
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Cited by 46 (2 self)
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As Bayesian networks are applied to more complex and realistic realworld applications, the development of more efficient inference algorithms working under realtime constraints is becoming more and more important. This paper presents a survey of various exact and approximate Bayesian network inference algorithms. In particular, previous research on realtime inference is reviewed. It provides a framework for understanding these algorithms and the relationships between them. Some important issues in realtime Bayesian networks inference are also discussed.