# Estimating Certain Integral Probability Metric (IPM) is as Hard as Estimating under the IPM

2 Nov 2019Tengyuan Liang

We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on $n$ independent samples from them. Curiously, we show that estimating the IPM itself between probability measures, is not significantly easier than estimating the probability measures under the IPM... (read more)

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