Weighted model counting has emerged as a prevalent approach for probabilistic inference. In this paper, we are interested in weighted DNF counting, or briefly, weighted #DNF, which admits a fully polynomial randomized approximation scheme, as shown by Karp and Luby. To this date, the best algorithm for approximating #DNF is due to Karp, Luby and Madras. The drawback of this algorithm is that it runs in quadratic time and hence is not suitable for fast online reasoning. To overcome this, we propose a novel approach that combines approximate model counting with deep learning. We conduct detailed experiments to validate our approach, and show that our model learns and generalizes from #DNF instances with a very high accuracy.
Knowledge compilation @cite_32 @cite_29 approaches, which push computational overhead to an offline compilation phase, enable WMC in linear time @cite_25 , but these approaches have limited scalability due to the inherent complexity of model counting. Approximate model counting methods such as hashing-based techniques @cite_9 @cite_16 @cite_14 provide probabilistic accuracy guarantees, but are not efficient in an online setting. We combine the advantages of both approaches to achieve fast online inference while providing more scalability. This falls in line with observations made recently in @cite_33 .
@cite_14 @cite_33 @cite_9 @cite_29 @cite_32 @cite_16 @cite_25
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Weighted model counting (WMC) on a propositional knowledge base is an effective and general approach to probabilistic inference in a variety of formalisms, including Bayesian and Markov Networks. However, an inherent limitation of WMC is that it only admits the inference of discrete probability distributions. In this paper, we introduce a strict generalization of WMC called weighted model integration that is based on annotating Boolean and arithmetic constraints, and combinations thereof. This methodology is shown to capture discrete, continuous and hybrid Markov networks. We then consider the task of parameter learning for a fragment of the language. An empirical evaluation demonstrates the applicability and promise of the proposal. 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. Probabilistic inference via model counting has emerged as a scalable technique with strong formal guarantees, thanks to recent advances in hashing-based approximate counting. State-of-the-art hashing-based counting algorithms use an NP oracle (SAT solver in practice), such that the number of oracle invocations grows linearly in the number of variables n in the input constraint. We present a new approach to hashing-based approximate model counting in which the number of oracle invocations grows logarithmically in n, while still providing strong theoretical guarantees. We use this technique to design an algorithm for #CNF with strongly probably approximately correct (SPAC) guarantees, i.e. PAC guarantee plus expected return value matching the exact model count. Our experiments show that this algorithm outperforms state-of-the-art techniques for approximate counting by 1-2 orders of magnitude in running time. We also show that our algorithm can be easily adapted to give a new fully polynomial randomized approximation scheme (FPRAS) for #DNF. Harvesting relational facts from Web sources has received great attention for automatically constructing large knowledge bases. Stateof-the-art approaches combine pattern-based gathering of fact candidates with constraint-based reasoning. However, they still face major challenges regarding the trade-offs between precision, recall, and scalability. Techniques that scale well are susceptible to noisy patterns that degrade precision, while techniques that employ deep reasoning for high precision cannot cope with Web-scale data. This paper presents a scalable system, called PROSPERA, for high-quality knowledge harvesting. We propose a new notion of ngram-itemsets for richer patterns, and use MaxSat-based constraint reasoning on both the quality of patterns and the validity of fact candidates.We compute pattern-occurrence statistics for two benefits: they serve to prune the hypotheses space and to derive informative weights of clauses for the reasoner. The paper shows how to incorporate these building blocks into a scalable architecture that can parallelize all phases on a Hadoop-based distributed platform. Our experiments with the ClueWeb09 corpus include comparisons to the recent ReadTheWeb experiment. We substantially outperform these prior results in terms of recall, with the same precision, while having low run-times.