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Median-of-Means as an Extremal Convex Estimator and a Nonconvex Route to the Trimmed Oracle — arXiv:2609.01689

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.01689
License (as archived): CC0-1.0
Archived: 2026-10-17T04:59:15.382Z
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Median-of-Means as an Extremal Convex Estimator and a Nonconvex Route to the Trimmed Oracle — arXiv:2609.01689 — arXiv (en), https://arxiv.org/abs/2609.01689 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_186e68a6741b (Metraipolis archive dc_186e68a6741b, sha256 cf8d353dcea5d42acca7110b0e2355db2ce8a2b42b5cf1f2e7f9da55ac726d0e)

BibTeX

@misc{dc186e68a6741b,
  title = {Median-of-Means as an Extremal Convex Estimator and a Nonconvex Route to the Trimmed Oracle — arXiv:2609.01689},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.01689},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_186e68a6741b; sha256 cf8d353dcea5d42acca7110b0e2355db2ce8a2b42b5cf1f2e7f9da55ac726d0e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.01689. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We revisit median-of-means estimation from a deterministic optimization viewpoint and develop a family of block-Lp estimators for robust learning with heavy-tailed and adversarially corrupted data. In a block contamination model with at least a fraction 1 minus epsilon of good blocks, we first show that every convex block M-estimator has worst-case robustness constant at least 1 divided by 1 minus 2 epsilon. This matches the classical median-of-means bound and proves that the trimmed-block oracle constant 1 divided by 1 minus epsilon cannot be attained within the convex class. We then introduce a nonconvex block-Lp family for p between 0 and 1 and derive finite-sample deterministic robustness bounds for all global minimizers. As p decreases from 1 toward 0, these bounds continuously approach the trimmed-block oracle constant. For sufficiently small p, the global minimizers coincide with those of the oracle under a mild separation condition. We also show that the block-Lp objectives have a benign landscape, with all local minima remaining close to the truth and no bad basins. Combining these results with block-level concentration yields sub-Gaussian deviation bounds under finite 2 plus delta moments and high-dimensional extensions to robust mean estimation and sparse regression.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-03 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.01689 — 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 2026-10-17T04:09:43.284Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-03?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).