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Robust Bayes-like estimation of the distribution of a determinantal process — arXiv:2611.09426

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.09426
License (as archived): CC0-1.0
Archived: 2026-11-09T22:42:43.025Z
SHA-256 of the archived text: 3902e621b474fe118a9788e010a653ca2eddfe621c6a38aed6f4172842ca9a2d
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How to cite

Robust Bayes-like estimation of the distribution of a determinantal process — arXiv:2611.09426 — arXiv (en), https://arxiv.org/abs/2611.09426 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_69effbcd624d (Metraipolis archive dc_69effbcd624d, sha256 3902e621b474fe118a9788e010a653ca2eddfe621c6a38aed6f4172842ca9a2d)

BibTeX

@misc{dc69effbcd624d,
  title = {Robust Bayes-like estimation of the distribution of a determinantal process — arXiv:2611.09426},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.09426},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_69effbcd624d; sha256 3902e621b474fe118a9788e010a653ca2eddfe621c6a38aed6f4172842ca9a2d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.09426. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We consider the problem of estimating the distribution of a determinantal process (DP) on a measured space from the observation of $n$ independent copies of it. Our estimator is obtained by sampling from a $T$-posterior distribution associated with a suitable prior, and we establish non-asymptotic risk bounds for the Hellinger loss which hold with high probability. These bounds remain valid when the data are only independent rather than i.i.d., and when the model is misspecified, which makes the estimator robust, for instance, to the presence of a small fraction of outliers. For determinantal projection processes of rank $k$ whose kernels are associated with $k$-dimensional subspaces of a $D$-dimensional space, Haar priors on Grassmannians lead to a rate of order $\sqrt{k(D-k)\log n/n}$, and model selection extends this result to infinite-dimensional settings. For general DPs, we introduce priors based on the spectral decomposition of the kernel that combine uniform distributions on the eigenvalues with Haar measures on Stiefel manifolds. When the underlying space is finite with $N$ elements, we obtain a rate of order $N\sqrt{\log n/n}$, without any assumption on the kernel, and derive that the $2^{N}$ principal minors of the kernel can be estimated simultaneously. Finally, for translation-invariant DPs on the torus $\mathbb{T}^d$, we obtain rates that only depend on the smoothness of the kernel at the origin and that are adaptive with respect to it. Combined with a new lower bound on the Hellinger distance between such DPs, these rates also yield estimators of the kernel in $\mathbb{L}_2$.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.ST, nuovi lavori del giorno).
Categorie arXiv: Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2611.09426 — 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 2026-11-09T22:35:47.240Z dalla pagina https://arxiv.org/list/math.ST/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).