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The Silhouette Operator: Identifiability of Low-Rank Measures from One-Dimensional Projections — arXiv:2610.09687

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.09687
License (as archived): CC0-1.0
Archived: 2026-10-08T12:37:03.394Z
SHA-256 of the archived text: 25e41c419422de9bff8b53177455417f52bc5bb6cf5212c9558df95ea00d4cc1
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How to cite

The Silhouette Operator: Identifiability of Low-Rank Measures from One-Dimensional Projections — arXiv:2610.09687 — arXiv (en), https://arxiv.org/abs/2610.09687 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fbdbae8280eb (Metraipolis archive dc_fbdbae8280eb, sha256 25e41c419422de9bff8b53177455417f52bc5bb6cf5212c9558df95ea00d4cc1)

BibTeX

@misc{dcfbdbae8280eb,
  title = {The Silhouette Operator: Identifiability of Low-Rank Measures from One-Dimensional Projections — arXiv:2610.09687},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.09687},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fbdbae8280eb; sha256 25e41c419422de9bff8b53177455417f52bc5bb6cf5212c9558df95ea00d4cc1},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.09687. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Structured recovery phenomena, such as restricted isometry properties in compressed sensing, have shown that high-dimensional objects can often be reconstructed from remarkably low-dimensional linear measurements. This work develops an analogous recovery framework for low-rank signed measures on $\mathbb{R}^2$, defined here as measures that can be expressed as finite sums of product measures with one-dimensional factors. The framework is based on linear operators, termed "silhouette operators," that map a measure to a fixed finite collection of one-dimensional linear pushforwards. The main results show that a suitably chosen collection of $2k$ projected marginals suffices to identify every compactly supported rank-$\le k$ signed measure, that this number is optimal, and that the projection directions cannot be chosen arbitrarily. The framework is also extended to higher-dimensional sums of product measures by establishing sufficient conditions under which collections of pairwise marginals identify the full model. Building on this framework, a computationally efficient estimator, termed "silhouette mixture estimation" (SME), is introduced for constructing a low-rank empirical measure from data by matching its one-dimensional projected marginals to the corresponding empirical marginals in Wasserstein distance. When combined with one-dimensional density estimators, SME yields an efficient nonparametric density estimator that performs strongly relative to a range of parametric, nonparametric, and deep-learning baselines in settings of moderate dimension and sample size.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Statistics Theory (math.ST) ; Information Theory (cs.IT); Machine Learning (cs.LG); Functional Analysis (math.FA); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2610.09687 — 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 2026-10-08T12:14:15.413Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).