mlsanityData to 7 Oct 2026

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

arXiv 1911.00730 ↗First posted 2 Nov 2019math.ST stat.ML stat.THcited by 11

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Abstract (arXiv)

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.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Nov 2019.

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Citing papers per year: 2021: 3; 2022: 2; 2023: 3; 2024: 0; 2025: 3.

11 papers.

  1. 2021Neural Estimation of Statistical Divergencescited by 25
  2. 2021Non-Asymptotic Performance Guarantees for Neural Estimation of mathsff-Divergencescited by 15
  3. 2023Sample Complexity Bounds for Estimating Probability Divergences under Invariancescited by 11
  4. 2021Reversible Gromov-Monge Sampler for Simulation-Based Inferencecited by 10
  5. 2023Adversarially Balanced Representation for Continuous Treatment Effect Estimationcited by 10
  6. 2023The Representation Jensen-Shannon Divergencecited by 9
  7. 2022Online Learning to Transport via the Minimal Selection Principlecited by 6
  8. 2025Scalable Sobolev IPM for Probability Measures on a Graphcited by 1
  9. 2022Unified Perspective on Probability Divergence via Maximum Likelihood Density Ratio Estimation: Bridging KL-Divergence and Integral Probability Metricscited by 0
  10. 2025Generalized Sobolev IPM for Graph-Based Measurescited by 0
  11. 2025Distributional Shrinkage I: Universal Denoiser Beyond Tweedie's Formulacited by 0