发表机构
University of Bristol（布里斯托大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出通过Stein位移场参数化密度比的方法，将分布偏移的统计与动力学描述统一于凸优化问题，衍生出前向、后向两种推理算法，在分布偏移等任务中验证了方法的优劣。
AI 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迁移到另一个分布。尽管两者提供互补的见解，但它们通常被分开估计，且将其中一个转换为另一个需要后处理。在本文中，我们通过将目标分布相对于基分布的密度比参数化为作用于基分布的位移场来估计：对数比被建模为基分布的Stein算子作用于该场的负值，再加上一个归一化常数。这通过单个凸优化问题同时提供了分布偏移的统计和动力学描述。迭代此估计-迁移步骤得到两种推理算法：前向迁移（push-forward）移动模型并校正预训练的采样器而无需重新训练，而后向迁移（pull-back）将数据移近基分布并逐层拟合变换模型。将其应用于基于模拟的推理中的分布偏移以及非线性独立成分分析，说明了该方法的优势与局限性。
英文摘要
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 inference algorithms: push-forward moves the model and corrects a pretrained sampler without retraining it, whereas pull-back moves the data closer to the base and fits a transformation model one layer at a time. Applications to distribution shift in simulation-based inference and to nonlinear independent component analysis illustrate the benefits and limitations of the approach.
