Derives non-asymptotic error bounds for standard, defensive, and self-normalized importance sampling with random KDE proposals from geometrically ergodic Markov chains, separating n^{-1/2} Monte Carlo error from MIAE/MISE proposal error.
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Sobolev-ball constraints on the hypothesis class achieve minimax rates for score estimation on the torus and, under conjecture, for generative modeling.
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Error Bounds for Importance Sampling with Estimated Proposal Distributions
Derives non-asymptotic error bounds for standard, defensive, and self-normalized importance sampling with random KDE proposals from geometrically ergodic Markov chains, separating n^{-1/2} Monte Carlo error from MIAE/MISE proposal error.
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Optimal score function estimation via derivatives constraints
Sobolev-ball constraints on the hypothesis class achieve minimax rates for score estimation on the torus and, under conjecture, for generative modeling.