Gadat, Sébastien Gerchinovitz, Sébastien Marteau, Clément

We consider the binary supervised classification problem with the Gaussian functional model introduced in [7]. Taking advantage of the Gaussian structure, we design a natural plug-in classifier and derive a family of upper bounds on its worst-case excess risk over Sobolev spaces. These bounds are parametrized by a separation distance quantifying th...

Rabier, Charles-Elie

In Quantitative Trait Locus detection, selective genotyping is a way to reduce costs due to genotyping : only individuals with extreme phenotypes are genotyped. We focus here on statistical inference for selective genotyping. We study, in a very large framework, the performances of different tests suitable for selective genotyping. We proof that we...

Brault, Vincent Keribin, Christine Mariadassou, Mahendra

Latent Block Model (LBM) is a model-based method to cluster simultaneously the d columns and n rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have been proposed and are now well understood empirically, theoretical guarantees about their asymptotic behavior is rather...

Arbel, Julyan Favaro, Stefano

Gibbs-type random probability measures, or Gibbs-type priors, are arguably the most " natural " generalization of the celebrated Dirichlet prior. Among them the two parameter Poisson–Dirichlet prior certainly stands out for the mathematical tractability and interpretability of its predictive probabilities, which made it the natural candidate in sev...

Castellan, Gwenaëlle Cousien, Anthony Tran, Viet Chi

The global sensitivity analysis is a set of methods aiming at quantifying the contribution of an uncertain input parameter of the model (or combination of parameters) on the variability of the response. We consider here the estimation of the Sobol indices of order 1 which are commonly-used indicators based on a decomposition of the output's varianc...

Chzhen, Evgenii Hebiri, Mohamed Salmon, Joseph

A well-know drawback of l1-penalized estimators is the systematic shrinkage of the large coefficients towards zero. A simple remedy is to treat Lasso as a model-selection procedure and to perform a second refitting step on the selected support. In this work we formalize the notion of refitting and provide oracle bounds for arbitrary refitting proce...

Caron, Emmanuel

In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan (1973), who proved a Central Limit Theorem for the usual least square estimator under general conditions on the design and on the error process. Whatever the design satisfying Hannan's conditio...

Caron, E. Dede, S.
Published in
Mathematical Methods of Statistics

We consider the usual linear regression model in the case where the error process is assumed strictly stationary.We use a result of Hannan, who proved a Central Limit Theorem for the usual least squares estimator under general conditions on the design and the error process.We show that for a large class of designs, the asymptotic covariance matrix ...

Alquier, Pierre Guedj, Benjamin
Published in
Machine Learning

PAC-Bayesian learning bounds are of the utmost interest to the learning community. Their role is to connect the generalization ability of an aggregation distribution ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setl...

Rey, C. Hengl, N. Baup, S. Karrouch, M. Dufresne, A. Djeridi, H. Dattani, R. Pignon, F.

International audience