2024/04/26 by Julien Chhor, Chhor, Julien, Olga Klopp +3 · 2 citations
Computer Science · #Advanced Image Processing Techniques #FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2404.17209
openalex publication_date 2024/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study 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-Hölder 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 unknown support as well as to the smoothness β and to the unknown number of separable components K. We present efficient algorithms for computing our estimators.