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New research analyzes Sinkhorn estimator convergence for optimal transport potentials

By PulseAugur Editorial · [1 sources] ·

Researchers have developed a new method to analyze the statistical convergence of empirical Sinkhorn estimators for entropic optimal transport potentials. The study establishes a non-asymptotic statistical rate of n^{-1/2} for a fixed regularization parameter \(\\varepsilon>0\), but notes that the constant in this bound grows exponentially with \(1/\varepsilon\). To address this, the paper identifies geometric conditions that allow the estimator to maintain the n^{-1/2} rate with only a polynomial dependence on \(1/\varepsilon\), requiring a polynomial residual-stability estimate for the population Sinkhorn map. AI

IMPACT This research provides theoretical guarantees for the convergence of Sinkhorn estimators, potentially improving the efficiency and accuracy of optimal transport calculations in machine learning applications.

RANK_REASON The cluster contains an academic paper detailing a new theoretical finding in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

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

New research analyzes Sinkhorn estimator convergence for optimal transport potentials

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The cluster contains an academic paper detailing a new theoretical finding in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Denis Belomestny ·

    Uniform Statistical Convergence of Empirical Sinkhorn Potentials with Exponential and Polynomial Dependence on the Regularization Parameter

    arXiv:2608.29152v1 Announce Type: cross Abstract: We study the empirical Sinkhorn estimator of the entropic optimal transport potentials under the uniform loss. Since the potentials are only unique up to additive constants, we measure the error using the quotient supremum norm, d…

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