# 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…

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