Encoding CNFs to Empower Component Analysis

Chavira, Mark; Darwiche, Adnan

doi:10.1007/11814948_9

Cited by 10 publications

(29 citation statements)

References 3 publications

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“…Here, WMC by compilation was shown to efficiently solve many problems with evidence, where they could not be compiled without evidence and where they could not be solved by algorithms that exploit only topological structure, with or without evidence, even after applying classical evidence-exploitation techniques. Methods for increasing the decomposability of the generated CNF by applying structured resolution were described in [3]. The increase in decomposability allowed many networks to be compiled for the first time and significantly decreased the time and space required to compile networks that were accessible previously.…”

Section: Related Workmentioning

confidence: 99%

“…The increase in decomposability allowed many networks to be compiled for the first time and significantly decreased the time and space required to compile networks that were accessible previously. Many of the algorithms for this compilation approach are implemented in a publicly available tool called Ace, 3 which uses the c2d compiler [26]. 4 A system described in [16] leverages a state-of-the-art model counter called Cachet 5 to perform inference in a Bayesian network.…”

Section: Related Workmentioning

confidence: 99%

“…We now provide a second comparison not previously addressed in the literature, between WMC by search (performed by the Cachet model counter version 2.0 [16]) and WMC by compilation (performed by Ace v2.0 [3]). For each network in Table 8, we encoded the network using Cachet and then applied both Ace and Cachet to the generated CNF.…”

Section: Wmc By Knowledge Compilationmentioning

confidence: 99%

See 2 more Smart Citations

On probabilistic inference by weighted model counting

Chavira¹,

Darwiche²

2008

Artificial Intelligence

Self Cite

239

271

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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.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Wmc By Knowledge Compilationmentioning

confidence: 99%

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On probabilistic inference by weighted model counting

Chavira¹,

Darwiche²

2008

Artificial Intelligence

Self Cite

239

271

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show abstract

“…The parameter MAX-FLIPS limits how many flips are done before a restart, while the number of tries is upper bounded by MAX-TRIES. 5 The parameter p N controls the noise level. Applying noise amounts to taking a random step with probability p N , and taking a greedy step using the chosen measure of gain with probability 1− p N .…”

Section: Simple Stochastic Greedy Searchmentioning

confidence: 99%

“…Recently, a connection between BNs and multi-linear functions has been made [10,11], supporting the compilation of BNs into arithmetic circuits [6,10,11]. The compilation of BNs into arithmetic circuits may rely on encoding of a BN into a CNF formula [10], which has been shown to take advantage of determinism [4] as well as other local structure in BNs [5]. Chavira and Darwiche encode a BN in the form of a weighted CNF theory, and investigate the effect of search versus compilation; different encodings; and local structure and evidence [5,7].…”

Section: Other Related Workmentioning

confidence: 99%

Portfolios in Stochastic Local Search: Efficiently Computing Most Probable Explanations in Bayesian Networks

2010

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Portfolio methods support the combination of different algorithms and heuristics, including stochastic local search (SLS) heuristics, and have been identified as a promising approach to solve computationally hard problems. While successful in experiments, theoretical foundations and analytical results for portfolio-based SLS heuristics are less developed. This article aims to improve the understanding of the role of portfolios of heuristics in SLS. We emphasize the problem of computing most probable explanations (MPEs) in Bayesian networks (BNs). Algorithmically, we discuss a portfolio-based SLS algorithm for MPE computation, Stochastic Greedy Search (SGS). SGS supports the integration of different initialization operators (or initialization heuristics) and different search operators (greedy and noisy heuristics), thereby enabling new analytical and experimental results. Analytically, we introduce a novel Markov chain model tailored to portfolio-based SLS algorithms including SGS, thereby enabling us to analytically form expected hitting time results that explain empirical run time results. For a specific BN, we show the benefit of using a homogenous initialization portfolio. To further illustrate the portfolio approach, we consider novel additive search heuristics for handling determinism in the form of zero entries in conditional probability tables in BNs. Our additive approach adds rather than multiplies probabilities when computing the utility of an explanation. We motivate the additive measure by studying the dramatic impact of zero entries in conditional probability tables on the number of zero-probability explanations, which again complicates the search process. We consider the relationship between MAXSAT and MPE, and show that additive utility (or gain) is a generalization, to the probabilistic setting, of MAXSAT utility (or gain) used in the celebrated GSAT and WalkSAT algorithms and their descendants. Utilizing our Markov chain framework, we show that expected hitting time is a rational function-i.e. a ratio of two polynomials-of the probability of applying an additive search operator. Experimentally, we report on synthetically generated BNs as well as BNs from applications, and compare SGS's performance to that of Hugin, which performs BN inference by compilation to and propagation in clique trees. On synthetic networks, SGS speeds up computation by approximately two orders of magnitude compared to Hugin. In application networks, our approach is highly competitive in Bayesian networks with a high degree of determinism. In addition to showing that stochastic local search can be competitive with clique tree clustering, our empirical results provide an improved understanding of the circumstances under which portfoliobased SLS outperforms clique tree clustering and vice versa.

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Weighted Model Counting Without Parameter Variables

Dilkas

Belle

2021

Theory and Applications of Satisfiability Testing – SAT 2021

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Weighted model counting (WMC) is a powerful computational technique for a variety of problems, especially commonly used for probabilistic inference. However, the standard definition of WMC that puts weights on literals often necessitates WMC encodings to include additional variables and clauses just so each weight can be attached to a literal. This paper complements previous work by considering WMC instances in their full generality and using recent state-of-the-art WMC techniques based on pseudo-Boolean function manipulation, competitive with the more traditional WMC algorithms based on knowledge compilation and backtracking search. We present an algorithm that transforms WMC instances into a format based on pseudo-Boolean functions while eliminating around 43 % of variables on average across various Bayesian network encodings. Moreover, we identify sufficient conditions for such a variable removal to be possible. Our experiments show significant improvement in WMC-based Bayesian network inference, outperforming the current state of the art.

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Encoding CNFs to Empower Component Analysis

Cited by 10 publications

References 3 publications

On probabilistic inference by weighted model counting

On probabilistic inference by weighted model counting

Portfolios in Stochastic Local Search: Efficiently Computing Most Probable Explanations in Bayesian Networks

Weighted Model Counting Without Parameter Variables

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