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47
Loopy Belief Propagation for Approximate Inference: An Empirical Study
 In Proceedings of Uncertainty in AI
, 1999
"... Recently, researchers have demonstrated that "loopy belief propagation"  the use of Pearl's polytree algorithm in a Bayesian network with loops  can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performance of "Turbo ..."
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Cited by 466 (18 self)
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Recently, researchers have demonstrated that "loopy belief propagation"  the use of Pearl's polytree algorithm in a Bayesian network with loops  can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performance of "Turbo Codes"  codes whose decoding algorithm is equivalent to loopy belief propagation in a chainstructured Bayesian network. In this paper we ask: is there something special about the errorcorrecting code context, or does loopy propagation work as an approximate inference scheme in a more general setting? We compare the marginals computed using loopy propagation to the exact ones in four Bayesian network architectures, including two realworld networks: ALARM and QMR. We find that the loopy beliefs often converge and when they do, they give a good approximation to the correct marginals. However, on the QMR network, the loopy beliefs oscillated and had no obvious relationship ...
Inference in belief networks: A procedural guide
 International Journal of Approximate Reasoning
, 1996
"... Belief networks are popular tools for encoding uncertainty in expert systems. These networks rely on inference algorithms to compute beliefs in the context of observed evidence. One established method for exact inference onbelief networks is the Probability Propagation in Trees of Clusters (PPTC) al ..."
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Cited by 149 (6 self)
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Belief networks are popular tools for encoding uncertainty in expert systems. These networks rely on inference algorithms to compute beliefs in the context of observed evidence. One established method for exact inference onbelief networks is the Probability Propagation in Trees of Clusters (PPTC) algorithm, as developed byLauritzen and Spiegelhalter and re ned by Jensen et al. [1, 2, 3] PPTC converts the belief network into a secondary structure, then computes probabilities by manipulating the secondary structure. In this document, we provide a selfcontained, procedural guide to understanding and implementing PPTC. We synthesize various optimizations to PPTC that are scattered throughout the literature. We articulate undocumented, \open secrets " that are vital to producing a robust and e cient implementation of PPTC. We hope that this document makes probabilistic inference more accessible and a ordable to those without extensive prior exposure.
Control of Selective Perception Using Bayes Nets and Decision Theory
, 1993
"... A selective vision system sequentially collects evidence to support a specified hypothesis about a scene, as long as the additional evidence is worth the effort of obtaining it. Efficiency comes from processing the scene only where necessary, to the level of detail necessary, and with only the neces ..."
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Cited by 100 (1 self)
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A selective vision system sequentially collects evidence to support a specified hypothesis about a scene, as long as the additional evidence is worth the effort of obtaining it. Efficiency comes from processing the scene only where necessary, to the level of detail necessary, and with only the necessary operators. Knowledge representation and sequential decisionmaking are central issues for selective vision, which takes advantage of prior knowledge of a domain's abstract and geometrical structure and models for the expected performance and cost of visual operators. The TEA1 selective vision system uses Bayes nets for representation and benefitcost analysis for control of visual and nonvisual actions. It is the highlevel control for an active vision system, enabling purposive behavior, the use of qualitative vision modules and a pointable multiresolution sensor. TEA1 demonstrates that Bayes nets and decision theoretic techniques provide a general, reusable framework for constructi...
Random Algorithms for the Loop Cutset Problem
 Journal of Artificial Intelligence Research
, 1999
"... We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called RepeatedWGuessI, outputs a minimum loop cutset, after O(c ..."
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Cited by 81 (2 self)
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We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called RepeatedWGuessI, outputs a minimum loop cutset, after O(c \Delta 6 k kn) steps, with probability at least 1 \Gamma (1 \Gamma 1 6 k ) c6 k , where c ? 1 is a constant specified by the user, k is the size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm, called WRA, often finds a loop cutset that is closer to the minimum loop cutset than the ones found by the best deterministic algorithms known. 1
Parameter adjustment in Bayes networks. The generalized noisy ORgate
 IN PROCEEDINGS OF THE 9TH CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
, 1993
"... Spiegelhalter and Lauritzen [15] studied sequential learning in Bayesian networks and proposed three models for the representation of conditional probabilities. A forth model, shown here, assumes that the parameter distribution is given by a product of Gaussian functions and updates them from ..."
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Cited by 70 (12 self)
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Spiegelhalter and Lauritzen [15] studied sequential learning in Bayesian networks and proposed three models for the representation of conditional probabilities. A forth model, shown here, assumes that the parameter distribution is given by a product of Gaussian functions and updates them from the and messages of evidence propagation. We also generalize the noisy ORgate for multivalued variables, develop the algorithm to compute probability in time proportional to the number of parents (even in networks with loops) and apply the learning model to this gate.
Topological Parameters for timespace tradeoff
 Artificial Intelligence
, 1996
"... In this paper we propose a family of algorithms combining treeclustering with conditioning that trade space for time. Such algorithms are useful for reasoning in probabilistic and deterministic networks as well as for accomplishing optimization tasks. By analyzing the problem structure it will be p ..."
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Cited by 58 (12 self)
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In this paper we propose a family of algorithms combining treeclustering with conditioning that trade space for time. Such algorithms are useful for reasoning in probabilistic and deterministic networks as well as for accomplishing optimization tasks. By analyzing the problem structure it will be possible to select from a spectrum the algorithm that best meets a given timespace specification. 1 INTRODUCTION Topologybased algorithms for constraint satisfaction and probabilistic reasoning fall into two distinct classes. One class is centered on treeclustering, the other on cyclecutset decomposition. Treeclustering involves transforming the original problem into a treelike problem that can then be solved by a specialized treesolving algorithm [ Mackworth and Freuder, 1985; Pearl, 1986 ] . The treeclustering algorithm is time and space exponential in the induced width (also called tree width) of the problem's graph. The transforming algorithm identifies subproblems that together ...
Localized Partial Evaluation of Belief Networks
, 1995
"... Most algorithms for propagating evidence through belief networks have been exact and exhaustive: they produce an exact (pointvalued) marginal probability for every node in the network. Often, however, an application will not need information about every node in the network nor will it need exact pr ..."
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Cited by 43 (1 self)
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Most algorithms for propagating evidence through belief networks have been exact and exhaustive: they produce an exact (pointvalued) marginal probability for every node in the network. Often, however, an application will not need information about every node in the network nor will it need exact probabilities. We present the localized partial evaluation (LPE) propagation algorithm, which computes interval bounds on the marginal probability of a specified query node by examining a subset of the nodes in the entire network. Conceptually, LPE ignores parts of the network that are "too far away" from the queried node to have much impact on its value. LPE has the "anytime" property of being able to produce better solutions (tighter intervals) given more time to consider more of the network. 1 Introduction Belief networks provide a way of encoding knowledge about the probabilistic dependencies and independencies of a set of variables in some domain. Variables are encoded as nodes in the ne...
Inference in Bayesian Networks
, 1999
"... A Bayesian network is a compact, expressive representation of uncertain relationships among parameters in a domain. In this article, I introduce basic methods for computing with Bayesian networks, starting with the simple idea of summing the probabilities of events of interest. The article introduce ..."
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Cited by 31 (0 self)
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A Bayesian network is a compact, expressive representation of uncertain relationships among parameters in a domain. In this article, I introduce basic methods for computing with Bayesian networks, starting with the simple idea of summing the probabilities of events of interest. The article introduces major current methods for exact computation, briefly surveys approximation methods, and closes with a brief discussion of open issues.
Local Conditioning in Bayesian Networks
 Artificial Intelligence
, 1996
"... Local conditioning (LC) is an exact algorithm for computing probability in Bayesian networks, developed as an extension of Kim and Pearl's algorithm for singlyconnected networks. A list of variables associated to each node guarantees that only the nodes inside a loop are conditioned on the variable ..."
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Cited by 28 (6 self)
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Local conditioning (LC) is an exact algorithm for computing probability in Bayesian networks, developed as an extension of Kim and Pearl's algorithm for singlyconnected networks. A list of variables associated to each node guarantees that only the nodes inside a loop are conditioned on the variable which breaks it. The main advantage of this algorithm is that it computes the probability directly on the original network instead of building a cluster tree, and this can save time when debugging a model and when the sparsity of evidence allows a pruning of the network. The algorithm is also advantageous when some families in the network interact through AND/OR gates. A parallel implementation of the algorithm with a processor for each node is possible even in the case of multiplyconnected networks. 1 Introduction A Bayesian network is an acyclic directed graph in which every node represents a random variable, together with a probability distribution such that P (x 1 ; : : : ; x n ) = ...
Maximal Prime Subgraph Decomposition of Bayesian Networks
 IEEE Transactions on Systems, Man, and Cybernetics, B
, 1999
"... In this paper we present a method for decomposition of Bayesian networks into their maximal prime subgraphs. The correctness of the method is proven and results relating the maximal prime subgraph decomposition to the maximal complete subgraphs of the moral graph of the original Bayesian network ..."
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Cited by 28 (0 self)
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In this paper we present a method for decomposition of Bayesian networks into their maximal prime subgraphs. The correctness of the method is proven and results relating the maximal prime subgraph decomposition to the maximal complete subgraphs of the moral graph of the original Bayesian network are presented. The maximal prime subgraphs of a Bayesian network can be organized as a tree which can be used as the computational structure for lazy propagation. We have also identified a number of tasks performed on Bayesian networks that can benefit from maximal prime subgraph decomposition. These tasks include divide and conquer triangulation, hybrid propagation algorithms combining exact and approximative inference techniques, and incremental construction of junction trees. Finally, we present the results of a series empirical evaluations relating the accumulated number of variables in maximal prime subgraphs of equal size to the size of the maximal prime subgraphs. 1 1