## Les conférenciers pléniers

#### Patricia Reynaud-Bouret (Univ. Nice)

Title :

Some concentration inequalities that are useful in statistics on point processes

Presentation en pdf

Abstract: I will describe some examples in genomics and in neuroscience where one needs to find different fully data-driven adaptive statistical methods for testing or for estimation. In all those examples, the key is to find concentration inequalities which either allow to very precisely calibrate the tuning parameter or to deeply understand how quantiles of test statistics are behaving. The main concentration tools are either "Talagrand" type inequalities for counting processes, Bernstein or Rosenthal type inequalities, or U-statistics - chaos inequalities.

#### Pierre Del Moral (Univ. Bordeaux)

Title :

Concentration inequalities for Feynman-Kac particle models and their applications

Presentation en pdf

Abstract: In this lecture we present some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution models, particle free energies, as well as backward Markov chain particle models. We illustrate these results with a series of topics related to computational physics and biology, stochastic optimization, signal processing and Bayesian statistics, and many other probabilistic machine learning algorithms. Special emphasis is given to the stochastic modeling, and to the quantitative performance analysis of a series of advanced Monte Carlo methods, including particle filters, genetic type island models, Markov bridge models, and interacting particle Markov chain Monte Carlo methodologies.

#### Nicolas Vayatis (Ens Cachan)

Title :

Applications of concentration inequalities for statistical ranking problems

Presentation en pdf

Abstract: The mathematical foundations of statistical learning theory heavily relies on concentration inequalities and empirical processes techniques. Learning an order relation over a Banach space involves performance measures which have higher order statistics, such as rank statistics, as empirical counterparts. The classical questions of consistency, universal and fast rates of convergence require dedicated tools which involve projection arguments and concentration inequalities for U- and R-processes. In the talk, we will present some results and open problems motivated by statistical problems of major interest.

#### Olivier Guedon (Univ. Paris Est)

Concentration phenomena in high dimensional geometry

Presentation en pdf

Abstract: I will describe some results about concentration of volume of high dimensional convex bodies obtained in the last decade. Central limit theorem for convex bodies is one of the main achievement of these series of work. I will also present some open problems, like the thin shell conjecture and the problem of spectral gap, a conjecture due to Kannan Lovasz and Simonovits. Extension of these results to new classes of probability measures, like Cauchy measure or more generally $\kappa$-concave measures will be discussed.

#### Roman Vershynin (Univ. Michigan, USA)

Title :

Probabilistic reasoning in compressed sensing

Presentation en pdf

Abstract: Compressed sensing is an area of information theory where one seeks to recover an unknown signal from few measurements. A signal is often modeled as a vector in R^n, and linear measurements are given as y = Ax where A is an m by n matrix. Best known results of compressed sensing are for random linear measurements, thus A is a random matrix. We will learn about some probabilistic successes and challenges in this area, with many connections to sampling theory, random matrix theory, and stochastic geometry.

#### Giovanni Peccati (Univ. Luxembourg, Luxembourg)

Title :

On probabilistic approximations and variance estimates

Presentation en pdf

Abstract: I will provide a survey of recent results concerning probabilistic approximations, obtained via the use of the Malliavin calculus of variations and the Stein and Chen-Stein methods. One advantage of this approach is that upper bounds are often expressed in terms of the variance of some random variable, so that well-known estimates (like e.g. given the Poincaré inequality and its generalizations) can be directly applied. I will also provide an overview of applications, ranging from fractional processes to random fields on homogeneous spaces, and from density estimates to geometric random graphs.

## Les lauréats du prix NEVEU (2010 et 2011)

#### Lauréats 2010: Sebastien Bubeck (Univ. Princeton (USA))

Title :

Minimax policies for adversarial multi-armed bandits.

Presentation en pdf

Abstract: In the recent years the multi-armed bandit problem has attracted a lot of attention in the theoretical learning community. This growing interest is a consequence of the large number of problems that can be modelized as a multi-armed bandit: web advertisement, dynamic pricing, online optimization, ect. Bandits algorithms are also used as building blocks in more complicated scenarios such as reinforcement learning, model selection problems, or games. In this talk I will focus on the so-called adversarial model for multi-armed bandits. I will show an algorithm that solves a long-standing open problem regarding the minimax rate for this framework. I will also discuss the recent extension of this algorithm to bandits with a very large, but structured, set of arms (such as paths on a graph).

#### Lauréats 2010: Kilian Raschel (Univ. de Tours )

Title :

Marches dans un quart de plan : approche analytique et applications

Presentation en pdf

Abstract: Au cours de cet exposé je présenterai quelques contributions à l'étude des marches (aléatoires ou non) dans un quart de plan. Nous présenterons d'abord les outils utiles à cette étude (utilisant fortement l'analyse complexe). Nous verrons alors de nombreuses applications des marches dans un quadrant : en probabilités (calcul des fonctions de Green, des fonctions harmoniques, de la loi du temps d'atteinte du bord) ; en combinatoire (énumération des marches confinées dans un quart de plan) ; en biologie des population (calcul des probabilités de survie de certaines populations de fleurs) ; en finance (carnet d'ordres markovien).

#### Lauréat 2011: Nicolas Curien (ENS Ulm)

Title :

Cartes planaires aléatoires

Presentation en pdf

Abstract: Dans cet exposé, nous effectuerons un rapide survol de l’étude probabiliste des grands graphes planaires aléatoires. Né au début des années 2000, motivé par des applications en physique théorique, combinatoire et géométrie, ce champ de recherche s’est beaucoup développé depuis. L’objectif principal est de comprendre la structure à grande échelle de graphes (ou cartes) planaires uniformes lorsque la taille tend vers l’infini. L’année dernière, Le Gall et Miermont ont montré qu’à la limite, une surface aléatoire (la carte brownienne) apparaît et peut être vue comme la généralisation du mouvement brownien en dimension 2. Nous ferons un rapide état de l’art sur le sujet et présenterons les problèmes ouverts et perspectives dans le domaine.