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46
Lifted firstorder probabilistic inference
 In Proceedings of IJCAI05, 19th International Joint Conference on Artificial Intelligence
, 2005
"... Most probabilistic inference algorithms are specified and processed on a propositional level. In the last decade, many proposals for algorithms accepting firstorder specifications have been presented, but in the inference stage they still operate on a mostly propositional representation level. [Poo ..."
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Cited by 88 (7 self)
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Most probabilistic inference algorithms are specified and processed on a propositional level. In the last decade, many proposals for algorithms accepting firstorder specifications have been presented, but in the inference stage they still operate on a mostly propositional representation level. [Poole, 2003] presented a method to perform inference directly on the firstorder level, but this method is limited to special cases. In this paper we present the first exact inference algorithm that operates directly on a firstorder level, and that can be applied to any firstorder model (specified in a language that generalizes undirected graphical models). Our experiments show superior performance in comparison with propositional exact inference. 1
New Advances in Compiling CNF into Decomposable Negation Normal Form
 In ECAI
, 2004
"... Abstract. We describe a new algorithm for compiling conjunctive normal form (CNF) into Deterministic Decomposable Negation Normal (dDNNF), which is a tractable logical form that permits model counting in polynomial time. The new implementation is based on latest techniques from both the SAT and OBD ..."
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Cited by 62 (14 self)
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Abstract. We describe a new algorithm for compiling conjunctive normal form (CNF) into Deterministic Decomposable Negation Normal (dDNNF), which is a tractable logical form that permits model counting in polynomial time. The new implementation is based on latest techniques from both the SAT and OBDD literatures, and appears to be orders of magnitude more efficient than previous algorithms for this purpose. We compare our compiler experimentally to state of the art model counters, OBDD compilers, and previous CNF2dDNNF compilers. 1
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 42 (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.
Performing bayesian inference by weighted model counting
 In Proceedings of the National Conference on Artificial Intelligence (AAAI
, 2005
"... Over the past decade general satisfiability testing algorithms have proven to be surprisingly effective at solving a wide variety of constraint satisfaction problem, such as planning and scheduling (Kautz and Selman 2003). Solving such NPcomplete tasks by “compilation to SAT ” has turned out to be a ..."
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Cited by 28 (0 self)
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Over the past decade general satisfiability testing algorithms have proven to be surprisingly effective at solving a wide variety of constraint satisfaction problem, such as planning and scheduling (Kautz and Selman 2003). Solving such NPcomplete tasks by “compilation to SAT ” has turned out to be an approach that is of both practical and theoretical interest. Recently, (Sang et al. 2004) have shown that state of the art SAT algorithms can be efficiently extended to the harder task of counting the number of models (satisfying assignments) of a formula, by employing a technique called component caching. This paper begins to investigate the question of whether “compilation to modelcounting ” could be a practical technique for solving realworld #Pcomplete problems, in particular Bayesian inference. We describe an efficient translation from Bayesian networks to weighted model counting, extend the best modelcounting algorithms to weighted model counting, develop an efficient method for computing all marginals in a single counting pass, and evaluate the approach on computationally challenging reasoning problems.
AND/OR branchandbound search for combinatorial optimization in graphical models
, 2008
"... We introduce a new generation of depthfirst BranchandBound algorithms that explore the AND/OR search tree using static and dynamic variable orderings for solving general constraint optimization problems. The virtue of the AND/OR representation of the search space is that its size may be far small ..."
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Cited by 26 (16 self)
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We introduce a new generation of depthfirst BranchandBound algorithms that explore the AND/OR search tree using static and dynamic variable orderings for solving general constraint optimization problems. The virtue of the AND/OR representation of the search space is that its size may be far smaller than that of a traditional OR representation, which can translate into significant time savings for search algorithms. The focus of this paper is on linear space search which explores the AND/OR search tree rather than the search graph and therefore make no attempt to cache information. We investigate the power of the minibucket heuristics within the AND/OR search space, in both static and dynamic setups. We focus on two most common optimization problems in graphical models: finding the Most Probable Explanation (MPE) in Bayesian networks and solving Weighted CSPs (WCSP). In extensive empirical evaluations we demonstrate that the new AND/OR BranchandBound approach improves considerably over the traditional OR search strategy and show how various variable ordering schemes impact the performance of the AND/OR search scheme.
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.
Speeding up inference in Markov logic networks by preprocessing to reduce the size of the resulting grounded network. IJCAI09
"... Statisticalrelational reasoning has received much attention due to its ability to robustly model complex relationships. A key challenge is tractable inference, especially in domains involving many objects, due to the combinatorics involved. One can accelerate inference by using approximation techni ..."
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Cited by 19 (2 self)
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Statisticalrelational reasoning has received much attention due to its ability to robustly model complex relationships. A key challenge is tractable inference, especially in domains involving many objects, due to the combinatorics involved. One can accelerate inference by using approximation techniques, “lazy ” algorithms, etc. We consider Markov Logic Networks (MLNs), which involve counting how often logical formulae are satisfied. We propose a preprocessing algorithm that can substantially reduce the effective size of MLNs by rapidly counting how often the evidence satisfies each formula, regardless of the truth values of the query literals. This is a general preprocessing method that loses no information and can be used for any MLN inference algorithm. We evaluate our algorithm empirically in three realworld domains, greatly reducing the work needed during subsequent inference. Such reduction might even allow exact inference to be performed when sampling methods would be otherwise necessary. 1
The Independent Choice Logic and Beyond
"... Abstract. The Independent Choice Logic began in the early 90’s as a way to combine logic programming and probability into a coherent framework. The idea of the Independent Choice Logic is straightforward: there is a set of independent choices with a probability distribution over each choice, and a l ..."
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Cited by 18 (5 self)
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Abstract. The Independent Choice Logic began in the early 90’s as a way to combine logic programming and probability into a coherent framework. The idea of the Independent Choice Logic is straightforward: there is a set of independent choices with a probability distribution over each choice, and a logic program that gives the consequences of the choices. There is a measure over possible worlds that is defined by the probabilities of the independent choices, and what is true in each possible world is given by choices made in that world and the logic program. ICL is interesting because it is a simple, natural and expressive representation of rich probabilistic models. This paper gives an overview of the work done over the last decade and half, and points towards the considerable work ahead, particularly in the areas of lifted inference and the problems of existence and identity. 1
SampleSearch: Importance Sampling in Presence of Determinism
, 2009
"... The paper focuses on developing effective importance sampling algorithms for mixed probabilistic and deterministic graphical models. The use of importance sampling in such graphical models is problematic because it generates many useless zero weight samples which are rejected yielding an inefficient ..."
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Cited by 14 (3 self)
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The paper focuses on developing effective importance sampling algorithms for mixed probabilistic and deterministic graphical models. The use of importance sampling in such graphical models is problematic because it generates many useless zero weight samples which are rejected yielding an inefficient sampling process. To address this rejection problem, we propose the SampleSearch scheme that augments sampling with systematic constraintbased backtracking search. We characterize the bias introduced by the combination of search with sampling, and derive a weighting scheme which yields an unbiased estimate of the desired statistics (e.g. probability of evidence). When computing the weights exactly is too complex, we propose an approximation which has a weaker guarantee of asymptotic unbiasedness. We present results of an extensive empirical evaluation demonstrating that SampleSearch outperforms other schemes in presence of significant amount of determinism.