Density Ratio Estimation with Stein Displacement Fields
Stein displacement fields estimate density ratios and distribution shift through one convex problem.
The paper estimates a density ratio by parametrizing it with a displacement field on a base distribution: the log-ratio is the negative Stein operator applied to that field, up to a normalizing constant. A single convex optimization therefore provides both statistical and dynamical descriptions of distribution shift. Iterating the estimate-and-move step yields push-forward correction of a pretrained sampler and pull-back fitting of transformations one layer at a time. Applications include simulation-based inference and nonlinear independent component analysis.
- Log-ratio equals a Stein operator applied to a displacement field.
- One convex problem yields ratio and transport descriptions.
- Push-forward corrects a sampler without retraining.
- Pull-back fits transformations one layer at a time.
From the original article
1 min read at arxiv.orgDensity 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.
By Song Liu · arxiv.org
A short excerpt; the article and its images belong to the publisher. Summary, key facts and assessment above are AI-written from the article and can be wrong.