1,357 research outputs found
Hashing-Based Approximate Probabilistic Inference in Hybrid Domains
In recent years, there has been considerable progress on fast randomized algorithms that ap-proximate probabilistic inference with tight toler-ance and confidence guarantees. The idea here is to formulate inference as a counting task over an annotated propositional theory, called weighted model counting (WMC), which can be parti-tioned into smaller tasks using universal hashing. An inherent limitation of this approach, how-ever, is that it only admits the inference of dis-crete probability distributions. In this work, we consider the problem of approximating inference tasks for a probability distribution defined over discrete and continuous random variables. Build-ing on a notion called weighted model integra-tion, which is a strict generalization of WMC and is based on annotating Boolean and arithmetic constraints, we show how probabilistic inference in hybrid domains can be put within reach of hashing-based WMC solvers. Empirical evalu-ations demonstrate the applicability and promise of the proposal.
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
Probabilistic Program Abstractions
Abstraction is a fundamental tool for reasoning about complex systems.
Program abstraction has been utilized to great effect for analyzing
deterministic programs. At the heart of program abstraction is the relationship
between a concrete program, which is difficult to analyze, and an abstract
program, which is more tractable. Program abstractions, however, are typically
not probabilistic. We generalize non-deterministic program abstractions to
probabilistic program abstractions by explicitly quantifying the
non-deterministic choices. Our framework upgrades key definitions and
properties of abstractions to the probabilistic context. We also discuss
preliminary ideas for performing inference on probabilistic abstractions and
general probabilistic programs
Closing the Gap Between Short and Long XORs for Model Counting
Many recent algorithms for approximate model counting are based on a
reduction to combinatorial searches over random subsets of the space defined by
parity or XOR constraints. Long parity constraints (involving many variables)
provide strong theoretical guarantees but are computationally difficult. Short
parity constraints are easier to solve but have weaker statistical properties.
It is currently not known how long these parity constraints need to be. We
close the gap by providing matching necessary and sufficient conditions on the
required asymptotic length of the parity constraints. Further, we provide a new
family of lower bounds and the first non-trivial upper bounds on the model
count that are valid for arbitrarily short XORs. We empirically demonstrate the
effectiveness of these bounds on model counting benchmarks and in a
Satisfiability Modulo Theory (SMT) application motivated by the analysis of
contingency tables in statistics.Comment: The 30th Association for the Advancement of Artificial Intelligence
(AAAI-16) Conferenc
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