Generalized multi-view model: Adaptive density estimation under low-rank constraints

Julien Chhor, Olga Klopp () and Alexandre B. Tsybakov
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Julien Chhor: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Olga Klopp: ESSEC Business School
Alexandre B. Tsybakov: IP Paris - Institut Polytechnique de Paris, ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris

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Abstract: Westudy the problem of bivariate discrete or continuous probability density estimation under low-rank constraints. For discrete distributions, we assume that the two-dimensional array to estimate is a low-rank probability matrix. In the continuous case, we assume that the density with respect to the Lebesgue measure satisfies a generalized multi-view model, meaning that it is β-H¨older and can be decomposed as a sum of K components, each of which is a product of one-dimensional functions. In both settings, we propose estimators that achieve, up to logarithmic factors, the minimax optimal convergence rates under such low-rank constraints. In the discrete case, the proposed estimator is adaptive to the rank K. In the continuous case, our estimator converges with the L1 rate min((K/n)β/(2β+1),n−β/(2β+2)) up to logarithmic factors, and it is adaptive to the un known support as well as to the smoothness β and to the unknown number of separable components K. We present efficient algorithms to compute our estimators.

Keywords: Minimax rate of; Convergence; Adaptive estimation; Low-rank models; Multi-view model; Density estimation (search for similar items in EconPapers)
Date: 2025-11
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Published in Journal of Machine Learning Research, 2025, 26, pp.1-52

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05621942

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