Monte Carlo algorithms often aim to draw from a distribution Ï€ by simulating a Markov chain with transition kernel P such that Ï€ is invariant under P . However, there are many situations for which itâ€¦ (More)

Abstract. The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni [6, 8] in the classification setting to more general problems of statistical inference. We show how toâ€¦ (More)

Let (X,Y ) be a random pair taking values in R Ã—R. In the so-called single-index model, one has Y = f â‹†(Î¸â‹†T X)+W , where f â‹† is an unknown univariate measurable function, Î¸â‹† is an unknown vector in Râ€¦ (More)

The PAC-Bayesian approach is a powerful set of techniques to derive non-asymptotic risk bounds for random estimators. The corresponding optimal distribution of estimators, usually called the Gibbsâ€¦ (More)

Abstract. This paper presents a new algorithm to perform regression estimation, in both the inductive and transductive setting. The estimator is defined as a linear combination of functions in aâ€¦ (More)

We consider the sparse regression model where the number of parameters p is larger than the sample size n. The difficulty when considering high-dimensional problems is to propose estimators achievingâ€¦ (More)

While Bayesian methods are extremely popular in statistics and machine learning, their application to massive datasets is often challenging, when possible at all. The classical MCMC algorithms areâ€¦ (More)

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching andâ€¦ (More)