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Learning under Target Shift: Optimal Density Ratio Estimation and Importance-Weighted Regression

arXiv · AI, language, vision and robotics · article · Sep 14, 2026 · UTC

We study density ratio estimation and importance-weighted regression under target shift with continuous outputs. Under target shift, the conditional distribution of the inputs given the outputs remains invariant across the training and test distributions, while the output marginal distribution may change. Although this problem has been extensively studied for discrete outputs, the continuous setting is substantially less understood: the importance weights are determined by an unknown density ratio function, for which existing estimation methods lack explicit finite-sample convergence rates. We

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