On probabilistic inference by weighted model counting
Artificial Intelligence
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In recent years, there has been much research on local search techniques for propositional inference. Some of the most successful procedures combine a form of random walk with a greedy bias. These procedures are quite effective in a number of problem domains, for example, constraint-based planning and scheduling, graph coloring, and hard random problem instances. However, backtrack-style procedures are often more effective in highly structured domains. In this dissertation, we present an approach for analyzing hidden variable dependencies that reduce the effectiveness of random-walk style algorithms. By introducing new constraints that capture these dependencies, we show that adding structural information can lead to an exponential speedup of local search inference methods. We also present empirical evidence showing that structures which lend themselves to this approach are embedded in many real-world inference problems, and that incorporating such constraints can yield significant improvements in our ability to solve practical problem instances. These methods can be extended to probabilistic-reasoning domains. Many forms of probabilistic reasoning, such as Bayesian inference, are computationally equivalent to counting or sampling models of propositional theories. We will show that near-uniform sampling and highly accurate approximate counting can be achieved by combining random-walk strategies with more traditional Monte Carlo Markov Chain (MCMC) methods.