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39
Fusion, Propagation, and Structuring in Belief Networks
 ARTIFICIAL INTELLIGENCE
, 1986
"... Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used to repre ..."
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Cited by 374 (7 self)
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Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used to represent the generic knowledge of a domain expert, and it turns into a computational architecture if the links are used not merely for storing factual knowledge but also for directing and activating the data flow in the computations which manipulate this knowledge. The first part of the paper deals with the task of fusing and propagating the impacts of new information through the networks in such a way that, when equilibrium is reached, each proposition will be assigned a measure of belief consistent with the axioms of probability theory. It is shown that if the network is singly connected (e.g. treestructured), then probabilities can be updated by local propagation in an isomorphic network of parallel and autonomous processors and that the impact of new information can be imparted to all propositions in time proportional to the longest path in the network. The second part of the paper deals with the problem of finding a treestructured representation for a collection of probabilistically coupled propositions using auxiliary (dummy) variables, colloquially called "hidden causes. " It is shown that if such a treestructured representation exists, then it is possible to uniquely uncover the topology of the tree by observing pairwise dependencies among the available propositions (i.e., the leaves of the tree). The entire tree structure, including the strengths of all internal relationships, can be reconstructed in time proportional to n log n, where n is the number of leaves.
Turbo decoding as an instance of Pearl’s belief propagation algorithm
 IEEE Journal on Selected Areas in Communications
, 1998
"... Abstract—In this paper, we will describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pear ..."
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Cited by 313 (15 self)
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Abstract—In this paper, we will describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pearl’s belief propagation algorithm. We shall see that if Pearl’s algorithm is applied to the “belief network ” of a parallel concatenation of two or more codes, the turbo decoding algorithm immediately results. Unfortunately, however, this belief diagram has loops, and Pearl only proved that his algorithm works when there are no loops, so an explanation of the excellent experimental performance of turbo decoding is still lacking. However, we shall also show that Pearl’s algorithm can be used to routinely derive previously known iterative, but suboptimal, decoding algorithms for a number of other errorcontrol systems, including Gallager’s
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 77 (1 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
Graphs, Causality, And Structural Equation Models
, 1998
"... Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers. ..."
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Cited by 44 (14 self)
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Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers.
Belief Networks Revisited
, 1994
"... this paper, Rumelhart presented compelling evidence that text comprehension must be a distributed process that combines both topdown and bottomup inferences. Strangely, this dual mode of inference, so characteristic of Bayesian analysis, did not match the capabilities of either the "certainty fact ..."
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Cited by 37 (6 self)
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this paper, Rumelhart presented compelling evidence that text comprehension must be a distributed process that combines both topdown and bottomup inferences. Strangely, this dual mode of inference, so characteristic of Bayesian analysis, did not match the capabilities of either the "certainty factors" calculus or the inference networks of PROSPECTOR  the two major contenders for uncertainty management in the 1970s. I thus began to explore the possibility of achieving distributed computation in a "pure" Bayesian framework, so as not to compromise its basic capacity to combine bidirectional inferences (i.e., predictive and abductive) . Not caring much about generality at that point, I picked the simplest structure I could think of (i.e., a tree) and tried to see if anything useful can be computed by assigning each variable a simple processor, forced to communicate only with its neighbors. This gave rise to the treepropagation algorithm reported in [15] and, a year later, the KimPearl algorithm [12], which supported not only bidirectional inferences but also intercausal interactions, such as "explainingaway." These two algorithms were described in Section 2 of Fusion.
Feedback set problems
 HANDBOOK OF COMBINATORIAL OPTIMIZATION
, 1999
"... ABSTRACT. This paper is a short survey of feedback set problems. It will be published in ..."
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Cited by 36 (1 self)
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ABSTRACT. This paper is a short survey of feedback set problems. It will be published in
Approximation Algorithms for the Feedback Vertex Set Problem with Applications to Constraint Satisfaction and Bayesian Inference
, 1998
"... A feedback vertex set of an undirected graph is a subset of vertices that intersects with the vertex set of each cycle in the graph. Given an undirected graph G with n vertices and weights on its vertices, polynomialtime algorithms are provided for approximating the problem of finding a feedback ve ..."
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Cited by 30 (3 self)
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A feedback vertex set of an undirected graph is a subset of vertices that intersects with the vertex set of each cycle in the graph. Given an undirected graph G with n vertices and weights on its vertices, polynomialtime algorithms are provided for approximating the problem of finding a feedback vertex set of G with a smallest weight. When the weights of all vertices in G are equal, the performance ratio attained by these algorithms is 4 \Gamma (2=n). This improves a previous algorithm which achieved an approximation factor of O( p log n) for this case. For general vertex weights, the performance ratio becomes minf2\Delta 2 ; 4 log 2 ng where \Delta denotes the maximum degree in G. For the special case of planar graphs this ratio is reduced to 10. An interesting special case of weighted graphs where a performance ratio of 4 \Gamma (2=n) is achieved is the one where a prescribed subset of the vertices, so called blackout vertices, is not allowed to participate in any feedback verte...
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 27 (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 ) = ...
Approximation Algorithms for the Vertex Feedback Set Problem with Applications to Constraint Satisfaction and Bayesian Inference
"... A vertex feedback set of an undirected graph is a subset of vertices that intersects with the vertex set of each cycle in the graph. Given an undirected graph G with n vertices and weights on its vertices, polynomialtime algorithms are provided for approximating the problem of finding a vertex feed ..."
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Cited by 26 (5 self)
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A vertex feedback set of an undirected graph is a subset of vertices that intersects with the vertex set of each cycle in the graph. Given an undirected graph G with n vertices and weights on its vertices, polynomialtime algorithms are provided for approximating the problem of finding a vertex feedback set of G with a smallest weight. When the weights of all vertices in G are equal, the performance ratio attained by these algorithms is 4 (2/n). This improves a previous algorithm which achieved an approximation factor of G for this case. For general vertex weights, the performance ratio becomes min{2A², 41og, n} where A denotes the maximum degree in G. For the special case of planar graphs this ratio is reduced to 10. An interesting special case of weighted graphs where a performance ratio of 4 (2/n) is achieved is