This paper is concerned with the detection of multiple changepoints in the joint distribution of independent categorical variables. The procedures introduced rely on model selection and are based on a penalized least-squares criterion. Their performance is assessed from a nonasymptotic point of view. Using a special collection of models, a preliminary estimator is built. According to an existin...

This paper introduces the concept of random context representations for the transition probabilities of a finitealphabet stochastic process. Processes with these representations generalize context tree processes (a.k.a. variable length Markov chains), and are proven to coincide with processes whose transition probabilities are almost surely continuous functions of the (infinite) past. This is s...

This paper considers lossless uniquely decodable source codes for a class of distributions described by a ball with respect to the total variational distance, centered at a nominal distribution with a given radius. The coding problem is formulated using minimax techniques, in which the maximum of the average codeword length over the class of distributions is minimized subject to Kraft inequalit...

QP is the optimization of a quadratic function subject to linear equality and inequality constraints. It arises in multiple objective decision making where the departure of the actual decisions from their corresponding ideal, or bliss, value can be evaluated using a weighted quadratic norm as a measure of deviation. The formulation of mean-variance optimization of uncertain systems also leads t...

We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in non-parametric regression model with heteroscedastic Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a PAC-Bayesian type inequality that leads to sharp oracle inequalities in discrete but also in continuous settings. The framework is general enough to cover the combinati...

We consider stationary hidden Markov models with finite state space and nonparametric modeling of the emission distributions. It has remained unknown until very recently that such models are identifiable. In this paper, we propose a new penalized least-squares estimator for the emission distributions which is statistically optimal and practically tractable. We prove a non asymptotic oracle ineq...

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 a given dictionary. Coefficients of the combinations are computed sequentially using projection on some simple sets. These sets are defined as confidence regions provided by a deviation (PAC) inequality o...

This article presents the results of experiments designed to gain insight into the effect of the minimax algorithm on the error of a heuristic evaluation function. Two types of effect of minimax are considered: (a) evaluation accuracy (are the minimax backed-up values more accurate than the heuristic values themselves?), and (b) decision accuracy (are moves played by deeper minimax search bette...

We search for behavioral rules that attain minimax regret under geometric discounting in the context of repeated decision making in a stationary environment where payo¤s belong to a given bounded interval. Rules that attain minimax regret exist and are optimal for Bayesian decision making under the prior where learning can be argued to be most di¢cult. Minimax regret can be attained by randomiz...

We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a regular lattice. In the time series setting, some procedures like AIC are proved to achieve optimal model selection among autoregressive models. However, there exists no such equivalent results of adaptivity in a spatial setting. By considering collections of Gaussian Markov random fields (GMRF) as a...