Under covariate shift with target data near a smooth d-dimensional manifold in D dimensions, the minimax regression rate switches between a manifold-dominated and a noise-dominated regime at a threshold set by source size, target size, smoothness, and d versus D.
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Phase Transition in Nonparametric Minimax Rates for Covariate Shifts on Approximate Manifolds
Under covariate shift with target data near a smooth d-dimensional manifold in D dimensions, the minimax regression rate switches between a manifold-dominated and a noise-dominated regime at a threshold set by source size, target size, smoothness, and d versus D.