Nonparametric estimation of a multivariate density under Kullback-Leibler loss with ISDE
@inproceedings{Pujol2022NonparametricEO, title={Nonparametric estimation of a multivariate density under Kullback-Leibler loss with ISDE}, author={Louis Pujol}, year={2022} }
In this paper, we propose a theoretical analysis of the algorithm ISDE, introduced in previous work. From a dataset, ISDE learns a density written as a product of marginal density estimators over a partition of the features. We show that under some hypotheses, the Kullback-Leibler loss between the proper density and the output of ISDE is a bias term plus the sum of two terms which goes to zero as the number of samples goes to infinity. The rate of convergence indicates that ISDE tackles the…
References
SHOWING 1-10 OF 11 REFERENCES
ISDE : Independence Structure Density Estimation
- Computer ScienceArXiv
- 2022
ISDE (Independence Structure Density Es-timation), an algorithm designed to estimate a multivariate density under Kullback-Leibler loss and the Independence Structure (IS) model, is proposed.
Multivariate density estimation under sup-norm loss: Oracle approach, adaptation and independence structure
- Mathematics
- 2013
This paper deals with the density estimation on R d under sup-norm loss. We provide a fully data-driven estimation procedure and establish for it a so-called sup-norm oracle inequality. The proposed…
On Kullback-Leibler loss and density estimation
- Mathematics
- 1987
On examine l'information de discrimination (ou perte de Kullback-Leibler) dans le contexte de l'estimation de densite par la methode du noyau et on montre que ses proprietes asymptotiques sont…
On density estimation in the view of Kolmogorov's ideas in approximation theory
- Mathematics, Computer Science
- 1989
The paper deals with upper and lower bounds for the quality of (probability) density estimation. Connections are established between these problems and the theory of approximation of functions.…
Concentration inequalities and model selection
- Mathematics
- 2007
Exponential and Information Inequalities.- Gaussian Processes.- Gaussian Model Selection.- Concentration Inequalities.- Maximal Inequalities.- Density Estimation via Model Selection.- Statistical…
Uniform Convergence Rate of the Kernel Density Estimator Adaptive to Intrinsic Volume Dimension
- Computer Science, MathematicsICML
- 2019
The volume dimension is proposed, called the volume dimension, to measure the intrinsic dimension of the support of a probability distribution based on the rates of decay of the probability of vanishing Euclidean balls and is useful for problems in geometric inference and topological data analysis.
Weak Convergence and Empirical Processes: With Applications to Statistics
- Mathematics
- 1996
This chapter discusses Convergence: Weak, Almost Uniform, and in Probability, which focuses on the part of Convergence of the Donsker Property which is concerned with Uniformity and Metrization.
Exponential Concentration for Mutual Information Estimation with Application to Forests
- Mathematics, Computer ScienceNIPS
- 2012
A new exponential concentration inequality for a plug-in estimator of the Shannon mutual information is proved, which can be used to optimally estimate the density function and graph of a distribution which is Markov to a forest graph.
A note on bounds for VC dimensions.
- Mathematics, Computer ScienceInstitute of Mathematical Statistics collections
- 2009
We provide bounds for the VC dimension of class of sets formed by unions, intersections, and products of VC classes of sets 𝒞(1),…,𝒞(m.