Estimating Certain Integral Probability Metrics (IPMs) Is as Hard as Estimating under the IPMs
Copyright policy )Estimating Certain Integral Probability Metrics (IPMs) Is as Hard as Estimating under the IPMs
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. We prove that the minimax optimal rates for these two problems are multiplicatively equivalent, up to a $\log \log (n)/\log (n)$ factor.
15 pages. arXiv admin note: substantial text overlap with arXiv:1908.10324
- University of Chicago United States
FOS: Computer and information sciences, Statistics - Machine Learning, FOS: Mathematics, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST)
FOS: Computer and information sciences, Statistics - Machine Learning, FOS: Mathematics, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST)
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