arXiv subjects

Louis Pujol

Publications and source records attributed to Louis Pujol.

3 recordsLinked to original sources

arXiv2022

Nonparametric estimation of a multivariate density under Kullback-Leibler loss with ISDE

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 curse of dimensionality by reducing the dimension from the one of the ambient space to the one of the biggest blocks in the partition. The constants reflect a combinatorial complexity reduction linked to the design of ISDE.

math.ST↗

arXiv2022

ISDE : Independence Structure Density Estimation

In this paper, we propose ISDE (Independence Structure Density Estimation), an algorithm designed to estimate a multivariate density under Kullback-Leibler loss and the Independence Structure (IS) model. IS tackles the curse of dimensionality by separating features into independent groups. We explain the construction of ISDE and present some experiments to show its performance on synthetic and real-world data. Performance is measured quantitatively by comparing empirical $\log$-likelihood with other density estimation methods and qualitatively by analyzing outputted partitions of variables. We also provide information about complexity and running time.

cs.LG↗

arXiv2019

Still no free lunches: the price to pay for tighter PAC-Bayes bounds

"No free lunch" results state the impossibility of obtaining meaningful bounds on the error of a learning algorithm without prior assumptions and modelling. Some models are expensive (strong assumptions, such as as subgaussian tails), others are cheap (simply finite variance). As it is well known, the more you pay, the more you get: in other words, the most expensive models yield the more interesting bounds. Recent advances in robust statistics have investigated procedures to obtain tight bounds while keeping the cost minimal. The present paper explores and exhibits what the limits are for obtaining tight PAC-Bayes bounds in a robust setting for cheap models, addressing the question: is PAC-Bayes good value for money?

cs.LG↗