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Pré-Publication, Document De Travail Année : 2021

ISDE : Independence Structure Density Estimation

Résumé

Density estimation appears as a subroutine in many learning procedures, so it is of crucial interest to have efficient methods to perform it in practical situations. Multidimensional density estimation faces the curse of dimensionality. To tackle this issue, a solution is to add a structural hypothesis through an undirected graphical model on the underlying distribution. We propose ISDE (Independence Structure Density Estimation) an algorithm designed to estimate a density and an undirected graphical model from a special family of graphs corresponding to an independence structure, where features can be separated into independent groups. It is designed for moderately high dimensional data (up to 15 features) and it can be used in parametric as well as nonparametric situations. Existing methods on nonparametric graph estimation focus on multidimensional dependencies only through pairwise ones. ISDE does not suffer from this restriction and can addresses structures not covered yet by available algorithms. In this paper, we present existing theory about independence structure, explain the construction of our algorithm and prove its effectiveness on simulated data both quantitatively, through measures of density estimation performance under Kullback-Leibler loss and qualitatively, in terms of recovering of independence structures. We also provide information about running time.
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Dates et versions

hal-03401530 , version 1 (25-10-2021)
hal-03401530 , version 2 (12-11-2021)
hal-03401530 , version 3 (17-03-2022)
hal-03401530 , version 4 (05-05-2022)

Identifiants

  • HAL Id : hal-03401530 , version 2

Citer

Louis Pujol. ISDE : Independence Structure Density Estimation. 2021. ⟨hal-03401530v2⟩
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