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Kernel discrepancy estimation minimax lower bound proven to be $n^{-1/2}$

By PulseAugur Editorial · [1 sources] ·

Researchers have established that the minimax lower bound for estimating kernel discrepancies, including MMD, HSIC, and KSD, is $n^{-1/2}$ on general topological spaces. This rate is achieved under mild kernel assumptions and confirms the parametric rate's optimality beyond finite-dimensional Euclidean settings with unbounded kernels. The findings also extend to the estimation of the mean embedding and centered cross-covariance operator, settling questions about optimal estimation for these kernel discrepancies. AI

IMPACT Establishes theoretical optimality for key distribution comparison methods used in machine learning.

RANK_REASON Academic paper published on arXiv detailing theoretical findings in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Kernel discrepancy estimation minimax lower bound proven to be $n^{-1/2}$

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Academic paper published on arXiv detailing theoretical findings in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Jose Cribeiro-Ramallo, Florian Kalinke, Zolt\'an Szab\'o ·

    Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD

    arXiv:2607.24235v1 Announce Type: new Abstract: Over the past 20 years, kernel discrepancies have been leveraged as a highly powerful tool for quantifying the disagreement of distributions, with numerous successful applications in two-sample, goodness-of-fit, and independence tes…

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