A multi-chart adversarial generative estimator is proven to achieve the minimax-optimal convergence rate for all Hölder Integral Probability Metrics simultaneously, on unknown manifolds of arbitrary topology.
In the case whereΨ(u) /∈g2 j (Bd(0, log(n)1/2 + 1)), we haveζg j (u) = 0 so let us focus on the case whereΨ(u) belongs tog2 j (Bd(0, log(n)1/2 + 1))
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Generative model for optimal density estimation on unknown manifold
A multi-chart adversarial generative estimator is proven to achieve the minimax-optimal convergence rate for all Hölder Integral Probability Metrics simultaneously, on unknown manifolds of arbitrary topology.