论文标题
通过可溶性循环分析贝叶斯网络
Analysis of Bayesian Networks via Prob-Solvable Loops
论文作者
论文摘要
可溶解的环路是概率的程序，具有随机变量和参数分布的多项式分配，为此，基于力矩的不变生成的完整自动化是可以决定的。在本文中，我们扩展了可解决的循环，具有编码贝叶斯网络（BNS）必不可少的新功能。我们表明，各种BN，例如离散，高斯，有条件的线性高斯和动态BNS，可以自然地编码为可溶解的循环。借助这些编码，我们可以自动解决与BN相关的几个问题，包括精确的推断，灵敏度分析，过滤和计算基于采样的过程中拒绝样品的预期数量。我们在可溶性循环分析中使用自动不变生成评估了许多BN基准测试的工作。
Prob-solvable loops are probabilistic programs with polynomial assignments over random variables and parametrised distributions, for which the full automation of moment-based invariant generation is decidable. In this paper we extend Prob-solvable loops with new features essential for encoding Bayesian networks (BNs). We show that various BNs, such as discrete, Gaussian, conditional linear Gaussian and dynamic BNs, can be naturally encoded as Prob-solvable loops. Thanks to these encodings, we can automatically solve several BN related problems, including exact inference, sensitivity analysis, filtering and computing the expected number of rejecting samples in sampling-based procedures. We evaluate our work on a number of BN benchmarks, using automated invariant generation within Prob-solvable loop analysis.
