Metraipolis › archive › dc_58df60d1fa12

Empirical Bayes linear regression in high dimensions: Method of moments and sub-linear sample complexity — arXiv:2608.16771

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.16771
License (as archived): CC0-1.0
Archived: 2026-10-18T20:21:14.145Z
SHA-256 of the archived text: d13eb24a984c98ee9e0ab040edfd328d483d8528445a629d6f346192b441e6bc
Stable URL of this page: https://metraipolis.com/documento/dc_58df60d1fa12

How to cite

Empirical Bayes linear regression in high dimensions: Method of moments and sub-linear sample complexity — arXiv:2608.16771 — arXiv (en), https://arxiv.org/abs/2608.16771 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_58df60d1fa12 (Metraipolis archive dc_58df60d1fa12, sha256 d13eb24a984c98ee9e0ab040edfd328d483d8528445a629d6f346192b441e6bc)

BibTeX

@misc{dc58df60d1fa12,
  title = {Empirical Bayes linear regression in high dimensions: Method of moments and sub-linear sample complexity — arXiv:2608.16771},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.16771},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_58df60d1fa12; sha256 d13eb24a984c98ee9e0ab040edfd328d483d8528445a629d6f346192b441e6bc},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.16771. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study empirical Bayes estimation of the prior in high-dimensional linear regression $\mathbf{y}=\mathbf{X}\mathbf{\beta}+\mathbf{\varepsilon}$, where the regression coefficients are drawn independently from an unknown sub-Gaussian prior. In contrast to the sequence model, the design matrix couples the latent coefficients, so that recovering the prior requires deconvolving it from both the noise and copies of itself. We introduce the \emph{Empirical Bayes Method of Moments} (EBMoM), a computationally efficient procedure for general designs that recursively estimates the prior moments through a lower-triangular system of estimating equations and runs in time $O(np^2)$. Under mild design conditions, satisfied in particular by a broad class of correlated random designs, we show that EBMoM consistently estimates a growing number of moments and hence the prior itself, provided that $n\geq p^{1-o(1)}$. A matching information-theoretic lower bound, valid for a broad class of designs, shows that this sub-linear sample complexity is optimal for nonparametric prior estimation. This improves on existing results for likelihood-based methods whose consistency requires a linear sample size $n=\Omega(p)$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-18 in math.ST).
Categorie arXiv: Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2608.16771 — 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 2026-10-18T19:45:21.130Z dalla pagina https://arxiv.org/catchup/math.ST/2026-08-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).