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Statistical Rates for Entropic Optimal Transport in the Discrete to SubGaussian Regime — arXiv:2609.26647

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.26647
License (as archived): CC0-1.0
Archived: 2026-10-08T15:11:37.141Z
SHA-256 of the archived text: fd294794a93149c60ee09d9a17134c5a9ee74160db7ef202826eee03d58bc2a4
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How to cite

Statistical Rates for Entropic Optimal Transport in the Discrete to SubGaussian Regime — arXiv:2609.26647 — arXiv (en), https://arxiv.org/abs/2609.26647 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3dee119dc481 (Metraipolis archive dc_3dee119dc481, sha256 fd294794a93149c60ee09d9a17134c5a9ee74160db7ef202826eee03d58bc2a4)

BibTeX

@misc{dc3dee119dc481,
  title = {Statistical Rates for Entropic Optimal Transport in the Discrete to SubGaussian Regime — arXiv:2609.26647},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.26647},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3dee119dc481; sha256 fd294794a93149c60ee09d9a17134c5a9ee74160db7ef202826eee03d58bc2a4},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.26647. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study statistical rates in entropic optimal transport in the semi-discrete regime where one measure has finite support and the other is subGaussian. Our main result establishes parametric convergence rates for the empirical dual potentials to their population counterparts, with no dimension dependence in the leading term. Our result relies on tailored strong concavity analysis of the semi-dual objective, coupled with specialized bounds for the semi-discrete potentials. As a consequence, we obtain fast rates for downstream quantities derived from the optimal coupling. Chiefly, the empirical barycentric projection achieves a squared-error rate $n^{-1}$, matching the fully compact case and improving over the less favorable $n^{-1/2}$ rate known for fully subGaussian settings. Altogether, these results may indicate a lower complexity adaptation phenomenon whereby the statistical complexity of the barycentric projection is governed by the discrete measure. As an application, we analyze Sinkhorn-EM, an EM-type algorithm in which the E-step is replaced by an entropic optimal transport problem. In a well-specified and balanced two-component Gaussian mixture model, we prove $\sqrt{n}$-consistency of the empirical iterates to their population counterparts for any fixed number of iterations, matching classical EM rates up to a $\sqrt{\log n}$ factor. Simulations support the theory.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-23 in cs.LG).
Categorie arXiv: Statistics Theory (math.ST) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.26647 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T14:37:29.584Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-23?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).