Harmonic map regression achieves the minimax rate n^{-2s/(2s+1)} for manifold responses while recovering the correct homotopy class of the regression map with high probability via energy barriers.
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Harmonic Map Regression: Rate-Optimal Nonparametric Estimation on Manifolds with Topological Recovery
Harmonic map regression achieves the minimax rate n^{-2s/(2s+1)} for manifold responses while recovering the correct homotopy class of the regression map with high probability via energy barriers.