发表机构
University of Warwick; University of Oxford; University of Hong Kong; Georgia Institute of Technology（华威大学; 牛津大学; 香港大学; 佐治亚理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于域缩减和Lewis权重采样的FPRAS，用于估计乘积分布混合模型及结构化概率电路间的全变差距离，实现了在维度和分量数上的多项式时间算法。
AI 中文摘要
计算简洁表示的高维分布之间的全变差（TV）距离通常是难以处理的。我们给出了乘积分布混合模型之间TV距离的FPRAS，并且更一般地，对于一类自然的结构化概率电路也给出了FPRAS。我们的主要技术是域缩减的一种新颖应用：给定一个由赋值索引的特征向量族，我们使用Lewis权重采样将赋值域替换为一个多项式大小的加权子集，该子集同时近似每个线性投影的绝对值之和。对于乘积分布的混合模型，我们跨坐标增量地构造这样的缩减域，获得了第一个运行时间在维度和混合分量数量上均为多项式的FPRAS。然后，我们将该方法扩展到具有共同结构化架构的平滑、确定性、结构化可分解的概率电路。
英文摘要
Computing the total variation (TV) distance between succinctly represented high-dimensional distributions is generally intractable. We give an FPRAS for TV distance between mixtures of product distributions and, more generally, for a natural class of structured probabilistic circuits. Our main technique is a novel application of domain reduction: Given a family of feature vectors indexed by assignments, we use Lewis-weight sampling to replace the assignment domain by a polynomial-size weighted subset that simultaneously approximates the sum of absolute values of every linear projection. For mixtures of product distributions, we construct such reduced domains incrementally over the coordinates, obtaining the first FPRAS with running time polynomial in both the dimension and the number of mixture components. We then extend the approach to smooth, structured-decomposable probabilistic circuits with a common structured architecture.
