[论文] Density Ratio Estimation with Stein Displacement Fields

论文概要

研究领域: ML
作者: Song Liu
发布时间: 2026-10-08
arXiv: 2610.12437

中文摘要

密度比从概率质量的角度量化分布偏移，而位移场从动力学的角度描述一个分布如何被传输到另一个分布。两者虽提供互补洞见，但通常被分别估计，相互转换需要后处理。本文通过在作用于基分布的位移场上参数化来估计目标分布与基分布之间的密度比：对数比被建模为基分布 Stein 算子作用于位移场的结果（差一个归一化常数）。这通过一个凸优化问题同时给出分布偏移的统计描述和动力学描述。迭代此"估计-移动"步骤得到两种推理算法：前推（push-forward）移动模型并修正预训练采样器而无需重训练；回拉（pull-back）将数据移近基分布并逐层拟合变换模型。在仿真推理中的分布偏移和非线性独立成分分析上的应用展示了该方法的收益与局限。

原文摘要

Density ratios quantify distribution shift from a probability-mass point of view, whereas displacement fields describe, from a dynamical point of view, how one distribution is transported onto another. Although both offer complementary insights, they are usually estimated separately, and converting one into the other requires post-processing. In this paper, we estimate the density ratio between a target and a base distribution by parametrizing it through a displacement field acting on the base: the log-ratio is modeled as minus the Stein operator of the base applied to the field, up to a normalizing constant. This gives both statistical and dynamical descriptions of the distribution shift through a single convex optimization problem. Iterating this estimate-and-move step gives two inferenc...

自动采集于 2026-10-10

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