Kernel-Matrix Determinant Estimates from stopped Cholesky Decomposition - Laboratoire Jean-Alexandre Dieudonné Accéder directement au contenu
Article Dans Une Revue Journal of Machine Learning Research Année : 2023

Kernel-Matrix Determinant Estimates from stopped Cholesky Decomposition

Résumé

Algorithms involving Gaussian processes or determinantal point processes typically require computing the determinant of a kernel matrix. Frequently, the latter is computed from the Cholesky decomposition, an algorithm of cubic complexity in the size of the matrix. We show that, under mild assumptions, it is possible to estimate the determinant from only a sub-matrix, with probabilistic guarantee on the relative error. We present an augmentation of the Cholesky decomposition that stops under certain conditions before processing the whole matrix. Experiments demonstrate that this can save a considerable amount of time while having an overhead of less than $5\%$ when not stopping early. More generally, we present a probabilistic stopping strategy for the approximation of a sum of known length where addends are revealed sequentially. We do not assume independence between addends, only that they are bounded from below and decrease in conditional expectation.

Dates et versions

hal-03359274 , version 1 (30-09-2021)

Identifiants

Citer

Simon Bartels, Wouter Boomsma, Jes Frellsen, Damien Garreau. Kernel-Matrix Determinant Estimates from stopped Cholesky Decomposition. Journal of Machine Learning Research, 2023. ⟨hal-03359274⟩
38 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More