A Minimax Theory of Nonparametric Regression Under Covariate Shift

Petr Zamolodtchikov

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arXiv · 2603.05897

A Minimax Theory of Nonparametric Regression Under Covariate Shift

Petr Zamolodtchikov

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Abstract

We consider nonparametric regression under covariate shift, where we observe samples from both the target distribution and a related but distinct source distribution. We introduce a novel object, the transfer function, and show that properties of its domain determine our minimax rates. Those exhibit a variety of regimes, including classical rates, governed by the better of source-only and target-only rates, as well as regimes in which the convergence rates exhibit multiplicative interactions between the sample sizes and are faster than the best-of-two benchmark. The rates are shown to be achieved up to logarithmic factors by a design-adaptive estimator. Compared with existing theory, our results cover the case in which covariates have unbounded support.

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Petr Zamolodtchikov. 2026-03-06. A Minimax Theory of Nonparametric Regression Under Covariate Shift. https://arxiv.org/abs/2603.05897

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