Results 1  10
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13
A differential approach to inference in Bayesian networks
 Journal of the ACM
, 2000
"... We present a new approach to inference in Bayesian networks which is based on representing the network using a polynomial and then retrieving answers to probabilistic queries by evaluating and differentiating the polynomial. The network polynomial itself is exponential in size, but we show how it ca ..."
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Cited by 112 (18 self)
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We present a new approach to inference in Bayesian networks which is based on representing the network using a polynomial and then retrieving answers to probabilistic queries by evaluating and differentiating the polynomial. The network polynomial itself is exponential in size, but we show how it can be computed efficiently using an arithmetic circuit that can be evaluated and differentiated in time and space linear in the circuit size. The proposed framework for inference subsumes one of the most influential methods for inference in Bayesian networks, known as the tree–clustering or jointree method, which provides a deeper understanding of this classical method and lifts its desirable characteristics to a much more general setting. We discuss some theoretical and practical implications of this subsumption. 1.
Compiling relational bayesian networks for exact inference
 International Journal of Approximate Reasoning
, 2004
"... We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available Primula tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evalua ..."
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Cited by 54 (11 self)
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We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available Primula tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating and differentiating these circuits in time linear in their size. We report on experimental results showing successful compilation and efficient inference on relational Bayesian networks, whose Primula–generated propositional instances have thousands of variables, and whose jointrees have clusters with hundreds of variables.
Complexity results and approximation strategies for map explanations
 Journal of Artificial Intelligence Research
, 2004
"... MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation (Pr), or the problem of computing the most probable explanatio ..."
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Cited by 33 (3 self)
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MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation (Pr), or the problem of computing the most probable explanation (MPE). This paper investigates the complexity of MAP in Bayesian networks. Specifically, we show that MAP is complete for NP PP and provide further negative complexity results for algorithms based on variable elimination. We also show that MAP remains hard even when MPE and Pr become easy. For example, we show that MAP is NPcomplete when the networks are restricted to polytrees, and even then can not be effectively approximated. Given the difficulty of computing MAP exactly, and the difficulty of approximating MAP while providing useful guarantees on the resulting approximation, we investigate best effort approximations. We introduce a generic MAP approximation framework. We provide two instantiations of the framework; one for networks which are amenable to exact inference (Pr), and one for networks for which even exact inference is too hard. This allows MAP approximation on networks that are too complex to even exactly solve the easier problems, Pr and MPE. Experimental results indicate that using these approximation algorithms provides much better solutions than standard techniques, and provide accurate MAP estimates in many cases. 1.
On probabilistic inference by weighted model counting
 Artificial Intelligence
"... A recent and effective approach to probabilistic inference calls for reducing the problem to one of weighted model counting (WMC) on a propositional knowledge base. Specifically, the approach calls for encoding the probabilistic model, typically a Bayesian network, as a propositional knowledge base ..."
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Cited by 22 (0 self)
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A recent and effective approach to probabilistic inference calls for reducing the problem to one of weighted model counting (WMC) on a propositional knowledge base. Specifically, the approach calls for encoding the probabilistic model, typically a Bayesian network, as a propositional knowledge base in conjunctive normal form (CNF) with weights associated to each model according to the network parameters. Given this CNF, computing the probability of some evidence becomes a matter of summing the weights of all CNF models consistent with the evidence. A number of variations on this approach have appeared in the literature recently, that vary across three orthogonal dimensions. The first dimension concerns the specific encoding used to convert a Bayesian network into a CNF. The second dimensions relates to whether weighted model counting is performed using a search algorithm on the CNF, or by compiling the CNF into a structure that renders WMC a polytime operation in the size of the compiled structure. The third dimension deals with the specific properties of network parameters (local structure) which are captured in the CNF encoding. In this paper, we discuss recent work in this area across the above three dimensions, and demonstrate empirically its practical importance in significantly expanding the reach of exact probabilistic inference. We restrict our discussion to exact inference and model counting, even though other proposals have been extended for approximate inference and approximate model counting.
An Extension of the Differential Approach for Bayesian Network Inference to Dynamic Bayesian Networks
 International Journal of Intelligent Systems
, 2004
"... We extend the differential approach to inference in Bayesian networks (BNs) (Darwiche, 2000) to handle specific problems that arise in the context of dynamic Bayesian networks (DBNs). We first summarize Darwiche's approach for BNs, which involves the representation of a BN in terms of a multivariate ..."
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Cited by 7 (3 self)
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We extend the differential approach to inference in Bayesian networks (BNs) (Darwiche, 2000) to handle specific problems that arise in the context of dynamic Bayesian networks (DBNs). We first summarize Darwiche's approach for BNs, which involves the representation of a BN in terms of a multivariate polynomial. We then show how procedures for the computation of corresponding polynomials for DBNs can be derived. These procedures permit not only an exact rollup of old time slices but also a constantspace evaluation of DBNs. The method is applicable to both forward and backward propagation, and it does not presuppose that each time slice of the DBN has the same structure. It is compatible with approximative methods for rollup and evaluation of DBNs. Finally, we discuss further ways of improving efficiency, referring as an example to a mobile system in which the computation is distributed over a normal workstation and a resourcelimited mobile device.
Exploiting withinclique factorizations in junctiontree algorithms
 In AISTATS
, 2010
"... It is wellknown that exact inference in treestructured graphical models can be accomplished efficiently by messagepassing operations following a simple protocol making use of the distributive law [Aji and McEliece, 2000,Kschischang et al., 2001], and that exact inference in arbitrary graphical mo ..."
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Cited by 4 (3 self)
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It is wellknown that exact inference in treestructured graphical models can be accomplished efficiently by messagepassing operations following a simple protocol making use of the distributive law [Aji and McEliece, 2000,Kschischang et al., 2001], and that exact inference in arbitrary graphical models can be solved by the JunctionTree Algorithm; its efficiency is determined by the size
Understanding the Scalability of Bayesian Network Inference using Clique Tree Growth Curves
"... Bayesian networks (BNs) are used to represent and ef ciently compute with multivariate probability distributions in a wide range of disciplines. One of the main approaches to perform computation in BNs is clique tree clustering and propagation. In this approach, BN computation consists of propagati ..."
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Cited by 2 (2 self)
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Bayesian networks (BNs) are used to represent and ef ciently compute with multivariate probability distributions in a wide range of disciplines. One of the main approaches to perform computation in BNs is clique tree clustering and propagation. In this approach, BN computation consists of propagation in a clique tree compiled from a Bayesian network. There is a lack of understanding of how clique tree computation time, and BN computation time in more general, depends on variations in BN size and structure. On the one hand, complexity results tell us that many interesting BN queries are NPhard or worse to answer, and it is not hard to nd application BNs where the clique tree approach in practice cannot be used. On the other hand, it is wellknown that treestructured BNs can be used to answer probabilistic queries in polynomial time. In this article, we develop an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, speci cally: (i) the ratio of the number of a BN's nonroot nodes to the number of root nodes, or (ii) the expected number of moral edges in their moral graphs. Our approach is based on combining analytical and experimental results. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for each set. For the special case of bipartite BNs, we consequently have two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, we systematically increase the degree of the root nodes in bipartite Bayesian networks, and nd that root clique growth is wellapproximated by Gompertz growth curves. It is believed that this research improves the understanding of the scaling behavior of clique tree clustering, provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms, and presents an aid for analytical tradeoff studies of clique tree clustering using growth curves.
Dynamic programming in influence diagrams with decision circuits
"... Decision circuits perform efficient evaluation of influence diagrams, building on the advances in arithmetic circuits for belief network inference [Darwiche, 2003; Bhattacharjya and Shachter, 2007]. We show how even more compact decision circuits can be constructed for dynamic programming in influen ..."
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Cited by 1 (1 self)
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Decision circuits perform efficient evaluation of influence diagrams, building on the advances in arithmetic circuits for belief network inference [Darwiche, 2003; Bhattacharjya and Shachter, 2007]. We show how even more compact decision circuits can be constructed for dynamic programming in influence diagrams with separable value functions and conditionally independent subproblems. Once a decision circuit has been constructed based on the diagram’s “global ” graphical structure, it can be compiled to exploit “local” structure for efficient evaluation and sensitivity analysis. 1
A Differential Semantics of Lazy AR Propagation
"... In this paper we present a differential semantics of Lazy AR Propagation (LARP) in discrete Bayesian networks. We describe how both single and multi dimensional partial derivatives of the evidence may easily be calculated from a junction tree in LARP equilibrium. We show that the simplicity of the c ..."
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Cited by 1 (1 self)
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In this paper we present a differential semantics of Lazy AR Propagation (LARP) in discrete Bayesian networks. We describe how both single and multi dimensional partial derivatives of the evidence may easily be calculated from a junction tree in LARP equilibrium. We show that the simplicity of the calculations stems from the nature of LARP. Based on the differential semantics we describe how variable propagation in the LARP architecture may give access to additional partial derivatives. The cautious LARP (cLARP) scheme is derived to produce a flexible cLARP equilibrium that offers additional opportunities for calculating single and multi dimensional partial derivatives of the evidence and subsets of the evidence from a single propagation. The results of an empirical evaluation illustrates how the access to a largely increased number of partial derivatives comes at a low computational cost.
Approximating the Partition Function by Deleting and then Correcting for Model Edges
"... We propose an approach for approximating the partition function which is based on two steps: (1) computing the partition function of a simplified model which is obtained by deleting model edges, and (2) rectifying the result by applying an edgebyedge correction. The approach leads to an intuitive ..."
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Cited by 1 (1 self)
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We propose an approach for approximating the partition function which is based on two steps: (1) computing the partition function of a simplified model which is obtained by deleting model edges, and (2) rectifying the result by applying an edgebyedge correction. The approach leads to an intuitive framework in which one can tradeoff the quality of an approximation with the complexity of computing it. It also includes the Bethe free energy approximation as a degenerate case. We develop the approach theoretically in this paper and provide a number of empirical results that reveal its practical utility. 1