Minimax rates for conditional distribution estimation on manifolds are established, with matching upper bounds from a hybrid wavelet and manifold estimator.
Using the partition of unity, one can glue constructions in the local charts to form a global construc- tion on the manifold
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Minimax Optimal Rates for Regression on Manifolds and Distributions
Minimax rates for conditional distribution estimation on manifolds are established, with matching upper bounds from a hybrid wavelet and manifold estimator.