一句话：提出高斯语义，用矩匹配高斯混合逼近概率程序语义，并证明通用逼近定理与二阶矩算法 SOGA。
概率程序的后验分布计算十分困难，缺乏通用解法。本文提出高斯语义（Gaussian Semantics），用高斯混合逼近有界概率程序的精确概率语义：通过一个映射为每个程序位置指定需匹配的矩阶。作者证明通用逼近定理——在温和条件下高斯语义可任意逼近精确语义；并针对任意阶矩匹配通常困难的问题，给出可解析匹配至二阶矩的近似方法 SOGA。在文献案例研究中，SOGA 在符号技术因复杂表达式或未化简积分而失效的模型上仍能给出准确估计；在协同过滤以及连续与离散分布混合的程序上，其精度和计算时间显著优于现有方法。
Computing the posterior distribution of a probabilistic program is a hard task for which no one-fit-for-all solution exists. We propose Gaussian Semantics, which approximates the exact probabilistic semantics of a bounded program by means of Gaussian mixtures. It is parametrized by a map that associates each program location with the moment order to be matched in the approximation. We provide two main contributions. The first is a universal approximation theorem stating that, under mild conditions, Gaussian Semantics can approximate the exact semantics arbitrarily closely. The second is an approximation that matches up to second-order moments analytically in face of the generally difficult problem of matching moments of Gaussian mixtures with arbitrary moment order. We test our second-order Gaussian approximation (SOGA) on a number of case studies from the literature. We show that it can provide accurate estimates in models not supported by other approximation methods or when exact symbolic techniques fail because of complex expressions or non-simplified integrals. On two notable classes of problems, namely collaborative filtering and programs involving mixtures of continuous and discrete distributions, we show that SOGA significantly outperforms alternative techniques in terms of accuracy and computational time.
@article{paperbot2648,
title = {Inference of Probabilistic Programs with Moment-Matching Gaussian Mixtures},
author = {Francesca Randone and Luca Bortolussi and Emilio Incerto and Mirco Tribastone},
journal = {Proceedings of the ACM on Programming Languages},
volume = {8},
number = {POPL},
year = {2024},
doi = {10.1145/3632905}
}