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85
AND/OR Search Spaces for Graphical Models
, 2004
"... The paper introduces an AND/OR search space perspective for graphical models that include probabilistic networks (directed or undirected) and constraint networks. In contrast to the traditional (OR) search space view, the AND/OR search tree displays some of the independencies present in the gr ..."
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Cited by 102 (44 self)
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The paper introduces an AND/OR search space perspective for graphical models that include probabilistic networks (directed or undirected) and constraint networks. In contrast to the traditional (OR) search space view, the AND/OR search tree displays some of the independencies present in the graphical model explicitly and may sometime reduce the search space exponentially. Indeed, most
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.
A Logical Approach to Factoring Belief Networks
"... We have recently proposed a tractable logical form, known as deterministic, decomposable negation normal form (dDNNF). We have shown that dDNNF supports a number of logical operations in polynomial time, including clausal entailment, model counting, model enumeration, model minimization, and proba ..."
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Cited by 51 (11 self)
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We have recently proposed a tractable logical form, known as deterministic, decomposable negation normal form (dDNNF). We have shown that dDNNF supports a number of logical operations in polynomial time, including clausal entailment, model counting, model enumeration, model minimization, and probabilistic equivalence testing. In this paper, we discuss another major application of this logical form: the implementation of multilinear functions (of exponential size) using arithmetic circuits (that are not necessarily exponential). Specifically, we show that each multi–linear function can be encoded using a propositional theory, and that each dDNNF of the theory corresponds to an arithmetic circuit that implements the encoded multi–linear function. We discuss the application of these results to factoring belief networks, which can be viewed as multi–linear functions as has been shown recently. We discuss the merits of the proposed approach for factoring belief networks, and present experimental results showing how it can handle efficiently belief networks that are intractable to structure–based methods for probabilistic inference.
On the Tractable Counting of Theory Models and its Application to Truth Maintenance and Belief Revision
 Journal of Applied NonClassical Logics
, 2000
"... We address the problem of counting the models of a propositional theory, under incremental changes to the theory. Specifically, we show that if a propositional theory is in a special form that we call smooth, deterministic, decomposable negation normal form (sdDNNF), then for any consistent set of ..."
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Cited by 49 (16 self)
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We address the problem of counting the models of a propositional theory, under incremental changes to the theory. Specifically, we show that if a propositional theory is in a special form that we call smooth, deterministic, decomposable negation normal form (sdDNNF), then for any consistent set of literals S, we can simultaneously count, in time linear in the size of , the models of: [ S; [ S [ flg: for every literal l 62 S; [ S n flg: for every literal l 2 S; [ S n flg [ f:lg: for every literal l 2 S.
Compiling Bayesian Networks with Local Structure
"... Recent work on compiling Bayesian networks has reduced the problem to that of factoring CNF encodings of these networks, providing an expressive framework for exploiting local structure. For networks that have local structure, large CPTs, yet no excessive determinism, the quality of the CNF encoding ..."
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Cited by 43 (7 self)
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Recent work on compiling Bayesian networks has reduced the problem to that of factoring CNF encodings of these networks, providing an expressive framework for exploiting local structure. For networks that have local structure, large CPTs, yet no excessive determinism, the quality of the CNF encodings and the amount of local structure they capture can have a significant effect on both the offline compile time and online inference time. We examine the encoding of such Bayesian networks in this paper and report on new findings that allow us to significantly scale this compilation approach. In particular, we obtain order–of–magnitude improvements in compile time, compile some networks successfully for the first time, and obtain orders– of–magnitude improvements in online inference for some networks with local structure, as compared to baseline jointree inference, which does not exploit local structure.
Casefactor diagrams for structured probabilistic modeling
 In Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI’04
, 2004
"... We introduce a probabilistic formalism subsuming Markov random fields of bounded tree width and probabilistic context free grammars. Our models are based on a representation of Boolean formulas that we call casefactor diagrams (CFDs). CFDs are similar to binary decision diagrams (BDDs) but are more ..."
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Cited by 42 (0 self)
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We introduce a probabilistic formalism subsuming Markov random fields of bounded tree width and probabilistic context free grammars. Our models are based on a representation of Boolean formulas that we call casefactor diagrams (CFDs). CFDs are similar to binary decision diagrams (BDDs) but are more concise than BDDs for circuits of bounded tree width and can concisely represent the set of parse trees over a given string under a given context free grammar (unlike BDDs). A probabilistic model consists of a CFD defining a feasible set of Boolean assignments and a weight (or cost) for each individual Boolean variable. We give an insideoutside algorithm for simultaneously computing the marginal of each Boolean variable, and a Viterbi algorithm for finding the minimum cost variable assignment. Both algorithms run in time proportional to the size of the CFD. 1 1
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.
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 32 (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.
When do Numbers Really Matter?
 Journal of Artificial Intelligence Research
, 2002
"... Common wisdom has it that small distinctions in the probabilities (parameters) quantifying a belief network do not matter much for the results of probabilistic queries. Yet, one can develop realistic scenarios under which small variations in network parameters can lead to significant changes in c ..."
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Cited by 28 (6 self)
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Common wisdom has it that small distinctions in the probabilities (parameters) quantifying a belief network do not matter much for the results of probabilistic queries. Yet, one can develop realistic scenarios under which small variations in network parameters can lead to significant changes in computed queries. A pending theoretical question is then to analytically characterize parameter changes that do or do not matter. In this paper, we study the sensitivity of probabilistic queries to changes in network parameters and prove some tight bounds on the impact that such parameters can have on queries. Our analytic results pinpoint some interesting situations under which parameter changes do or do not matter. These results are important for knowledge engineers as they help them identify influential network parameters. They also help explain some of the previous experimental results and observations with regards to network robustness against parameter changes.