arXiv：cs.LG· Song Liu·· 3 小时前
用 Stein 位移场估计密度比
Density Ratio Estimation with Stein Displacement Fields
AI 导读
该论文提出通过位移场参数化目标分布与基分布之间的密度比，将对数密度比建模为基分布 Stein 算子作用于该位移场的负值（至多相差归一化常数），从而用单个凸优化问题同时给出分布偏移的统计与动力学描述。
正文
Abstract: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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.12437 [stat.ML] |
| (or arXiv:2610.12437v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12437 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Song Liu Dr. [view email]
[v1]
Thu, 8 Oct 2026 17:57:33 UTC (55 KB)
来源：arXiv：cs.LG · arxiv.org