89 citations · 206 across the 15 of their papers we have counts for
15 papers
New bounds for -means and information -means
Gautier Appert, Olivier Catoni
In this paper, we derive a new dimension-free non-asymptotic upper bound for the quadratic -means excess risk related to the quantization of an i.i.d sample in a separable Hilbe…
Constant payoff in zero-sum stochastic games
Olivier Catoni, Miquel Oliu-Barton, Bruno Ziliotto
In a zero-sum stochastic game, at each stage, two adversary players take decisions and receive a stage payoff determined by them and by a controlled random variable representing th…
Dimension-free PAC-Bayesian bounds for the estimation of the mean of a random vector
Olivier Catoni, Ilaria Giulini
In this paper, we present a new estimator of the mean of a random vector, computed by applying some threshold function to the norm. Non asymptotic dimension-free almost sub-Gaussia…
Dimension-free PAC-Bayesian bounds for matrices, vectors, and linear least squares regression
Olivier Catoni, Ilaria Giulini
This paper is focused on dimension-free PAC-Bayesian bounds, under weak polynomial moment assumptions, allowing for heavy tailed sample distributions. It covers the estimation of t…
Markov substitute processes : a new model for linguistics and beyond
Olivier Catoni, Thomas Mainguy
We introduce Markov substitute processes, a new model at the crossroad of statistics and formal grammars, and prove its main property : Markov substitute processes with a given sup…
PAC-Bayesian bounds for the Gram matrix and least squares regression with a random design
Olivier Catoni
The topics dicussed in this paper take their origin inthe estimation of the Gram matrix of a random vector from a sample made of n independent copies. They comprise the estimation…