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arXiv 1206.3555cs.AIcs.DS
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递归概率规划推理的动态规划算法

A Dynamic Programming Algorithm for Inference in Recursive Probabilistic Programs

Massachusetts Institute of Technology(麻省理工学院);Stanford University(斯坦福大学)

Andreas Stuhlmüller, Noah D. Goodman

摘要:

本文描述了一种计算离散概率规划边际分布的动态规划算法。该算法对任意概率程序设计语言采用函数解释器,并将其转化为有效的边缘化器。由于直接缓存的子分布是不可能的递归的存在,我们建立一个子分布之间的依赖关系图。这个因子化的和积网络使得子问题之间的依赖性(可能是循环的)显式的,并且对应于边际分布的方程组。我们按拓扑顺序用不动点迭代法求解这些方程。我们说明了这个算法的例子用于教学概率模型,计算认知科学研究,博弈论。

英文摘要:

We describe a dynamic programming algorithm for computing the marginal distribution of discrete probabilistic programs. This algorithm takes a functional interpreter for an arbitrary probabilistic programming language and turns it into an efficient marginalizer. Because direct caching of sub-distributions is impossible in the presence of recursion, we build a graph of dependencies between sub-distributions. This factored sum-product network makes (potentially cyclic) dependencies between subproblems explicit, and corresponds to a system of equations for the marginal distribution. We solve these equations by fixed-point iteration in topological order. We illustrate this algorithm on examples used in teaching probabilistic models, computational cognitive science research, and game theory.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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