Conference Paper

A Dynamic Approach for MPE and Weighted MAX-SAT.

Conference: IJCAI 2007, Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, January 6-12, 2007
Source: DBLP


The problem of Most Probable Explanation (MPE) arises in the scenario of probabilistic inference: finding an assignment to all variables that has the maximum likelihood given some evidence. We consider the more general CNF-based MPE prob- lem, where each literal in a CNF-formula is asso- ciated with a weight. We describe reductions be- tween MPE and weighted MAX-SAT, and show that both can be solved by a variant of weighted model counting. The MPE-SAT algorithm is quite competitive with the state-of-the-art MAX-SAT, WCSP, and MPE solvers on a variety of problems.

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    • "Problems of probabilistic inference in Bayesian networks have already been encoded as weighted MAX- SAT problems and various algorithms, including MaxWalkSAT have been applied to them [6] [7]. Similar approaches combined with MCMC have been used for inference in Markov logic [5]. "
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    ABSTRACT: The problem of learning discrete Bayesian networks from data is encoded as a weighted MAX-SAT problem and the MaxWalkSat local search algorithm is used to address it. For each dataset, the per-variable summands of the (BDeu) marginal likelihood for different choices of parents ('family scores') are computed prior to applying MaxWalkSat. Each permissible choice of parents for each variable is encoded as a distinct propositional atom and the associated family score encoded as a 'soft' weighted single-literal clause. Two approaches to enforcing acyclicity are considered: either by encoding the ancestor relation or by attaching a total order to each graph and encoding that. The latter approach gives better results. Learning experiments have been conducted on 21 synthetic datasets sampled from 7 BNs. The largest dataset has 10,000 datapoints and 60 variables producing (for the 'ancestor' encoding) a weighted CNF input file with 19,932 atoms and 269,367 clauses. For most datasets, MaxWalkSat quickly finds BNs with higher BDeu score than the 'true' BN. The effect of adding prior information is assessed. It is further shown that Bayesian model averaging can be effected by collecting BNs generated during the search.
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    ABSTRACT: Inference in Bayes Nets (BAYES) is an important problem with numerous applications in probabilistic reasoning. Counting the number of satisfying assignments of a propositional formula (#SAT) is a closely related problem of fundamental theoretical importance. Both these problems, and others, are members of the class of sum-of-products (SUMPROD) problems. In this paper we show that standard backtracking search when augmented with a simple memoization scheme (caching) can solve any sum-of-products problem with time complexity that is at least as good any other state-of-the-art exact algorithm, and that it can also achieve the best known time-space tradeoff. Furthermore, backtracking's ability to utilize more flexible variable orderings allows us to prove that it can achieve an exponential speedup over other standard algorithms for SUMPROD on some instances. The ideas presented here have been utilized in a number of solvers that have been applied to various types of sum-of-product problems. These system's have exploited the fact that backtracking can naturally exploit more of the problem's structure to achieve improved performance on a range of probleminstances. Empirical evidence of this performance gain has appeared in published works describing these solvers, and we provide references to these works.
    Journal of Artificial Intelligence Research 01/2009; 34:391-442. DOI:10.1613/jair.2648 · 1.26 Impact Factor
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