用量子信息理论重构概率电路，实现更强大的生成建模。
A Quantum Information Theoretic Approach to Tractable Probabilistic Models
- 引入正幺正电路，将概率计算推广到半正定矩阵
- 支持多项式时间变量边缘化，优于传统概率电路
- 适合研究量子机器学习与高阶概率建模的学者
通过递归嵌套求和与乘积，概率电路近年来成为一类有吸引力的生成模型，因其可实现随机变量的多项式时间边缘化。本文利用量子信息理论框架研究此类机器学习模型，提出正幺正电路（PUnCs），将基于正实值概率的电路计算推广至半正定矩阵上的电路计算。结果表明，PUnCs严格推广了概率电路及近期提出的如半正定电路（PSD circuits）等模型。
原文摘要 · Abstract (English)
By recursively nesting sums and products, probabilistic circuits have emerged in recent years as an attractive class of generative models as they enjoy, for instance, polytime marginalization of random variables. In this work we study these machine learning models using the framework of quantum information theory, leading to the introduction of positive unital circuits (PUnCs), which generalize circuit evaluations over positive real-valued probabilities to circuit evaluations over positive semi-definite matrices. As a consequence, PUnCs strictly generalize probabilistic circuits as well as recently introduced circuit classes such as PSD circuits.
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