Density Ratio Estimation with Stein Displacement Fields

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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2610.12437 [stat.ML]

(or arXiv:2610.12437v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.12437 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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