Arnak Dalalyan (ENSAE)
Thursday, June 15th 2017, 10h
On the Exponentially Weighted Aggregate with the Laplace Prior
We study the statistical behaviour of the Exponentially Weighted Aggregate (EWA) in the problem of high-dimensional regression with fixed design. Under the assumption that the underlying regression vector is sparse, it is reasonable to use the Laplace distribution as a prior. The resulting estimator and, specifically, a particular instance of it referred to as the Bayesian lasso, was already used in the statistical literature because of its computational convenience, even though no thorough mathematical analysis of its statistical properties was carried out. The present work fills this gap by establishing sharp oracle inequalities for the EWA with the Laplace prior. These inequalities show that if the temperature parameter is small, the EWA with the Laplace prior satisfies the same type of oracle inequality as the lasso estimator does, as long as the quality of estimation is measured by the prediction loss. Extensions of the proposed methodology to the problem of prediction with low-rank matrices are considered.
Reference: Arnak S. Dalalyan, Edwin Grappin, Quentin Paris, arXiv:1611.08483.
Mitchell Luskin (University of Minnesota)
Monday October 17th, 2016, 14h
Mathematical Modelling of Incommensurate Materials
Incommensurate materials are found in crystals, liquid crystals, and quasi-crystals. Stacking a few layers of 2D materials such as graphene and molybdenum disulfide, for example, opens the possibility to tune the elastic, electronic, and optical properties of these materials. One of the main issues encountered in the mathematical modeling of layered 2D materials is that lattice mismatch and rotations between the layers destroys the periodic character of the system. This leads to complex commensurate-incommensurate transitions and pattern formation. Even basic concepts like the Cauchy-Born strain energy density, the electronic density of states, and the Kubo-Greenwood formulas for transport properties have not been given a rigorous analysis in the incommensurate setting. New approximate approaches will be discussed and the validity and efficiency of these approximations will be examined from mathematical and numerical analysis perspectives.
Common seminar CERMICS/IMAGINE
Tuesday June 7th, 10h
Emilie Kaufmann (CNRS)
Wednesday March 30th, 2016, 14h
Multi-armed bandit models: a tutorial (slides)
Reinforcement learning refers to the situation in which an agent learns to optimaly interact with his environment by trying to maximize rewards received during the interaction. In the simplest case, the interaction consists in repeatedly choosing actions that lead to some (possibly random) payoff. This situation can be described by a multi-armed bandit model. Even if this name refers to a gambler who tries to maximize its gain by sequentially choosing the arm of which slot-machine (or one-armed bandit) he wants to draw, bandit models were introduced to model clinical trials, and have been recently successfully applied to online content optimization. In this tutorial, I will present different types of bandit models and related algorithms (for choosing which action to play based on past observation. Under each of these model assumptions, I will try to define some optimality criterion, and introduce the tools to build optimal algorithms.
Hugo Touchette (National Institute for Theoretical Physics)
Monday November 30th, 2015, 14h
Théorie des grandes déviations : des mathématiques à la physique. (slides)
Cet exposé se veut un survol général de la théorie des grandes déviations et de ses applications en physique statistique. La première partie rappellera quelques sources intéressantes de cette théorie issues des mathématiques (Sanov, Varadhan) et de la physique (Boltzmann, Einstein, Lanford), et exposera les résultats essentiels de cette théorie. Dans la deuxième partie, quelques applications physiques seront présentées afin de démontrer l’utilité de la théorie des grandes déviations en physique statistique, tant pour étudier les systèmes à l’équilibre que hors équilibre. L’exposé ne supposera aucune connaissance préalable de physique statistique.