Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting

Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic guarantees are obtained in O(nm), where n denotes the number of variables, and m the number of clauses of the input DNF, but this is not scalable in practice. In this paper, we propose a neural model counting approach for weighted #DNF that combines approximate model counting with deep learning, and accurately approximates model counts in linear time when width is bounded. We conduct experiments to validate our method, and show that our model learns and generalizes very well to large-scale #DNF instances.Comment: To appear in Proceedings of the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20). Code and data available at: https://github.com/ralphabb/NeuralDNF

Flexible constrained sampling with guarantees for pattern mining

Pattern sampling has been proposed as a potential solution to the infamous pattern explosion. Instead of enumerating all patterns that satisfy the constraints, individual patterns are sampled proportional to a given quality measure. Several sampling algorithms have been proposed, but each of them has its limitations when it comes to 1) flexibility in terms of quality measures and constraints that can be used, and/or 2) guarantees with respect to sampling accuracy. We therefore present Flexics, the first flexible pattern sampler that supports a broad class of quality measures and constraints, while providing strong guarantees regarding sampling accuracy. To achieve this, we leverage the perspective on pattern mining as a constraint satisfaction problem and build upon the latest advances in sampling solutions in SAT as well as existing pattern mining algorithms. Furthermore, the proposed algorithm is applicable to a variety of pattern languages, which allows us to introduce and tackle the novel task of sampling sets of patterns. We introduce and empirically evaluate two variants of Flexics: 1) a generic variant that addresses the well-known itemset sampling task and the novel pattern set sampling task as well as a wide range of expressive constraints within these tasks, and 2) a specialized variant that exploits existing frequent itemset techniques to achieve substantial speed-ups. Experiments show that Flexics is both accurate and efficient, making it a useful tool for pattern-based data exploration.Comment: Accepted for publication in Data Mining & Knowledge Discovery journal (ECML/PKDD 2017 journal track

Distribution-Aware Sampling and Weighted Model Counting for SAT

Given a CNF formula and a weight for each assignment of values to variables, two natural problems are weighted model counting and distribution-aware sampling of satisfying assignments. Both problems have a wide variety of important applications. Due to the inherent complexity of the exact versions of the problems, interest has focused on solving them approximately. Prior work in this area scaled only to small problems in practice, or failed to provide strong theoretical guarantees, or employed a computationally-expensive maximum a posteriori probability (MAP) oracle that assumes prior knowledge of a factored representation of the weight distribution. We present a novel approach that works with a black-box oracle for weights of assignments and requires only an {\NP}-oracle (in practice, a SAT-solver) to solve both the counting and sampling problems. Our approach works under mild assumptions on the distribution of weights of satisfying assignments, provides strong theoretical guarantees, and scales to problems involving several thousand variables. We also show that the assumptions can be significantly relaxed while improving computational efficiency if a factored representation of the weights is known.Comment: This is a full version of AAAI 2014 pape

Simple Load Balancing for Distributed Hash Tables

Distributed hash tables have recently become a useful building block for a variety of distributed applications. However, current schemes based upon consistent hashing require both considerable implementation complexity and substantial storage overhead to achieve desired load balancing goals. We argue in this paper that these goals can b e achieved more simply and more cost-effectively. First, we suggest the direct application of the "power of two choices" paradigm, whereby an item is stored at the less loaded of two (or more) random alternatives. We then consider how associating a small constant number of hash values with a key can naturally b e extended to support other load balancing methods, including load-stealing or load-shedding schemes, as well as providing natural fault-tolerance mechanisms

Sampling Techniques for Boolean Satisfiability

Boolean satisfiability ({\SAT}) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the problems of generating satisfying uniformly at random, and of counting the total number of satisfying assignments have also attracted significant theoretical and practical interest over the years. Prior work offered heuristic approaches with very weak or no guarantee of performance, and theoretical approaches with proven guarantees, but poor performance in practice. We propose a novel approach based on limited-independence hashing that allows us to design algorithms for both problems, with strong theoretical guarantees and scalability extending to thousands of variables. Based on this approach, we present two practical algorithms, {\UniformWitness}: a near uniform generator and {\approxMC}: the first scalable approximate model counter, along with reference implementations. Our algorithms work by issuing polynomial calls to {\SAT} solver. We demonstrate scalability of our algorithms over a large set of benchmarks arising from different application domains.Comment: MS Thesis submitted to Rice Universit