Séminaire de Statistique

CREST, ENSAE,

Université Paris-Saclay

CMAP,

Ecole Polytechnique

Organisateurs:

C. Butucea

A. B. Tsybakov

E.  Moulines

M. Rosenbaum

 

Lundi / Monday 14h - 15h15 – SALLE 3001 ENSAE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sept 11 2017

Arnak Dalalyan

ENSAE

Title : User-friendly bounds for sampling from a log-concave density using Langevin Monte Carlo

 

Abstract :  We will present new bounds on the sampling error in the case where the target distribution has a smooth and log-concave density. These bounds are established for the Langevin Monte Carlo and its discretized versions involving the Hessian matrix of the log-density. We will also discuss the case where accurate evaluation of the gradient is impossible.

Sept 18 2017

Séminaire Parisien de Statistique - IHP

 

Sept 25 2017

Mathias Trabs

Université de Hamburg

Title : Volatility estimation for stochastic PDE’s using high-frequency observations

 

Abstract : We study the parameter estimation for parabolic, linear, second order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of the grid in the time variable goes to zero. Focusing on volatility estimation, we provide an explicit and easy to implement method of moments estimator based on the squared increments of the process. The estimator is consistent and admits a central limit theorem. Starting from a representation of the solution as an infinite factor model, the theory considerably differs from the statistics for semi-martingales literature. The performance of the method is illustrated in a simulation study.


This is joint work with Markus Bibinger.

 

 

 

Oct 2 2017

Nicolas Marie

Modal’X (Paris 10)/ ESME Sudria

Title : Estimation non-paramétrique dans les équations différentielles dirigées par le mouvement brownien fractionnaire.

 

Abstract : Après avoir introduit quelques notions de calcul stochastique trajectoriel, l’exposé présentera un estimateur type Nadaraya-Watson de la fonction de drift d’une équation différentielle dirigée par un bruit multiplicatif fractionnaire. Afin d’établir la consistance de l’estimateur, les résultats d’ergodicité de Hairer et Ohashi (2007) seront énoncés et expliqués. Une fois sa consistence établie, la question de la vitesse de convergence de l’estimateur sera abordée. Il s’agit d’un travail en collaboration avec F. Comte.

Oct 9 2017

Zoltan Szabo

Ecole Polytechnique

Title : Characteristic Tensor Kernels

 

Abstract : Maximum mean discrepancy (MMD) and Hilbert-Schmidt independence criterion (HSIC) are popular techniques in data science to measure the difference and the independence of random variables, respectively. 

Thanks to their kernel-based foundations, MMD and HSIC are applicable on a variety of domains including documents, images, trees, graphs, time series, mixture models, dynamical systems, sets, distributions, permutations. Despite their tremendous practical success, quite little is known about when HSIC characterizes independence and MMD with tensor kernel can discriminate probability distributions, in terms of the 
contributing kernel components. In this talk, I am going to present a complete answer to this question, with conditions which are often easy to verify in practice. [Joint work with Bharath K. Sriperumbudur (PSU). 

Preprint: https://arxiv.org/abs/1708.08157]

Oct 16 2017

Séminaire Parisien de Statistique - IHP

 

Oct 23 2017

Philip Thompson

ENSAE

Cancelled

Oct 30 2017

Vacances

 

 

 

 

Nov 6 2017

Martin Kroll

ENSAE

Title : On minimax optimal and adaptive estimation of linear functionals in inverse Gaussian sequence space models

 

Abstract : We consider an inverse problem in a Gaussian sequence space model where the multiplication operator is not known but only available via noisy observations. Our aim is not to reconstruct the solution itself but the value of a linear functional of the solution. In our setup the optimal rate depends on two different noise levels, the noise level concerning the observation of the transformed solution and the noise level concerning the noisy observation of the operator.  We consider this problem from a minimax point of view and obtain upper and lower bounds under smoothness assumptions on the multiplication operator and the unknown solution.  Finally, we sketch an approach to the adaptive estimation in the given model using a method combining both model selection and the Goldenshluger-Lepski method.


This is joint work in progress with Cristina Butucea (ENSAE) and Jan Johannes (Heidelberg)

 

Nov 13 2017

Séminaire Parisien de Statistique - IHP

 

Nov 20 2017

Olivier Collier

Université Paris Nanterre

Title : Estimation robuste de la moyenne en temps polynômial

 

Abstract : Il s'agit de résultats obtenus en collaboration avec Arnak Dalalyan. Quand les observations sont polluées par la présence d'outliers, il n'est plus souhaitable d'estimer l'espérance par la moyenne empirique. Des méthodes optimales ont été trouvées, comme la profondeur de Tuckey dans le modèle dit de contamination. Cependant, ce dernier estimateur n'est pas calculable en temps polynômial. Dans un modèle gaussien, nous remarquerons que l'estimation de la moyenne revient à l'estimation d'une fonctionnelle linéaire sous contrainte de sparsité de groupe. Il est alors naturel d'utiliser group-lasso. Nous pourrons alors noter plusieurs phénomènes intéressants : dans ce contexte, la sparsité par groupe permet un gain polynômial par rapport à la seule sparsité, alors que les études précédentes montraient au mieux un gain logarithmique, et il semble que l'estimation en temps polynômial ne puisse pas atteindre la performance optimale des méthodes en temps exponentiel.

Nov 27 2017

Elisabeth Gassiat

Université Paris-Sud

Title : Estimation of the proportion of explained variation in high dimensions.

 

Abstract : Estimation of heritability of a phenotypic trait based on genetic data may be set as estimation of the proportion of explained variation in high dimensional linear models. I will be interested in understanding the impact of:

— not knowing the sparsity of the regression parameter,

— not knowing the variance matrix of the covariates

on minimax estimation of heritability.

In the situation where the variance of the design is known, I will present an estimation procedure that adapts to unknown sparsity. 

when the variance of the design is unknown and no prior estimator of it is available,  I will show that  consistent estimation of heritability is impossible.

(Joint work with N. Verzelen, and PHD thesis of A. Bonnet).

 

 

 

 

Dec 4 2017

Philip Thomson

ENSAE

Title : Stochastic approximation with heavier tails

 

Abstract : We consider the solution of convex optimization and variational inequality problems via the stochastic approximation methodology where the gradient or operator can only be accessed through an unbiased stochastic oracle. First, we show that (non-asymptotic) convergence is possible with unbounded constraints and a "multiplicative noise" model: the oracle is Lipschitz continuous with a finite pointwise variance which may not be uniformly bounded (as classically assumed). In this setting, our bounds depend on local variances at solutions and the method uses noise reduction in an efficient manner: given a precision, it respects a near-optimal sample and averaging complexities of Polyak-Ruppert's method but attains the order of the (faster) deterministic iteration complexity. Second, we discuss a more "robust" version where the Lipschitz constant L is unknown but, in terms of error precision, near-optimal complexities are maintained. A price to pay when L is unknown is that a large sample regime is assumed (still respecting the complexity of the SAA estimator) and "non-martingale-like" dependencies are introduced. These dependencies are coped with an "iterative localization" argument based on empirical process theory and self-normalization. 

Joint work with A. Iusem (IMPA), A. Jofré (CMM-Chile) and R.I. Oliveira (IMPA).

Dec 11 2017

Jamal Najim

CNRS UPEM

Title : Grandes matrices de covariance empiriques 

 

Abstract : Les modèles de grandes matrices de covariance empirique ont été énormément étudiés depuis l’article fondateur de Marchenko et Pastur en 1967, qui ont décrit le comportement du spectre de telles matrices quand les deux dimensions (dimension des observations et taille de l’échantillon) croissent vers l’infini au même rythme. 

 

L’objectif de cet exposé sera dans un premier temps de présenter les résultats standards (et moins standards!) liés à ces modèles et les outils mathématiques d’analyse (principalement la transformée de Stieltjes). On insistera ensuite sur le cas particulier des « spiked models », modèles de grandes matrices de covariance dans lesquels quelques valeurs propres sont éloignées de la masse des valeurs propres de la matrice considérée. Ces « spiked models »  sont très populaires en finance, économétrie, traitement du signal, etc.

 

Enfin, on s’intéressera à des grandes matrices de covariance dont les observations sont issues d’un processus à mémoire longue. Pour de telles observations, on décria le comportement asymptotique et des fluctuations de la plus grande valeur propre. Ce travail est issu d’une collaboration avec F. Merlevède et P. Tian. 

 

Dec 18 2017

Pas de séminaire

 

 

 

 

Jan 8 2018

Eric Moulines

Ecole Polytechnique

Title : Algorithmes de simulation de Langevin

 

Abstract : Les algorithmes de Langevin ont connu récemment un vif regain d’intérêt dans la communauté de l’apprentissage statistique, suite aux travaux de M. Welling et Y.W. Teh (‘Bayesian learning via Stochastic gradient Langevin dynamics’, ICML, 2011). Cette méthode couplant approximation stochastique et méthode de simulation permet d’envisager la mise en œuvre de méthodes de simulation en grande dimension et pour des grands ensembles de données. Les applications sont très nombreuses à la fois dans les domaines «classiques » des statistiques bayésiennes (inférence bayésienne, choix de modèles) mais aussi en optimisation bayésienne.

Dans cet exposé, nous présenterons quelques travaux récents sur l’analyse de convergence de cet algorithme. Nous montrerons comment obtenir des bornes explicites de convergence en distance de Wasserstein et en variation totale dans différents cadres (fortement convexe, convexe différentiable, super-exponentiel, etc.). Nous nous intéresserons tout particulièrement à la dépendance de ces bornes dans la dimension du paramètre. Nous montrerons aussi comment étendre ces méthodes pour des fonctions convexes mais non différentiables en nous inspirant des méthodes de gradient proximaux.

 

Jan 15 2018

Séminaire Parisien de Statistique – IHP

 

Jan 22 2018

 

Data Science

Jan 29 2018

Anatoli Juditsky

Université de Grenoble-Alpes

Titre : Aggrégation des estimateurs à partir d’observations indirectes

 

Nous considérons le problème d’agrégation d'estimation adaptative dans le cas où des observations indirectes du signal sont disponibles. Nous proposons une approche au problème d’agrégation par tests quasi-optimaux d'hypothèses convexes basée sur la réduction du problème statistique d’agrégation à des problèmes d'optimisation convexe admettant une analyse et une mise en œuvre efficace.

On montre que cette approche conduit aux algorithmes quasi-optimaux dans le problème classique de l’agrégation - L_2 pour différents schémas d'observation (par exemple, observations gaussiennes indirectes, modèle d'observations de Poisson et échantillonnage à partir d’une loi discrète). Nous discutons également le lien avec le problème lié d’estimation adaptative.

 

 

 

 

Feb 5

2018

Frédéric Chazal

INRIA

Title: An introduction to persistent homology in Topological Data Analysis and the density of expected persistence diagrams.

 

Abstract: Persistence diagrams play a fundamental role in Topological Data Analysis (TDA) where they are used as topological descriptors of data represented as point cloud. They consist in discrete multisets of points in the plane $\R^2$ that can equivalently be seen as discrete measures in $\R^2$. In a first part of the talk, we will introduce the notions of persistent homology and persistence diagrams and show how they are built from point cloud data (so no knowledge in TDA is required to follow the talk). In the second part of the talk we will show a few properties of persistence diagrams when the data come as a random point cloud. In this case, persistence diagrams become random discrete measures and we will show that, in many cases, their expectation has a density with respect to Lebesgue measure in the plane and we will discuss its estimation.

This is a joint work with Vincent Divol (ENS Paris / Inria DataShape team)

 

Feb 12

2018

Séminaire Parisien de Statistique - IHP

 

Feb 19

2018

Laëtitia Comminges

Université Paris-Dauphine

Some effects in adaptive robust estimation under sparsity

 

Abstract:

Adaptive estimation in the sparse mean model and in sparse regression exhibits some interesting effects.

This paper considers estimation of a sparse target vector, of its $\ell_2$-norm and of the noise variance in the sparse linear model. We establish the optimal rates of adaptive estimation when adaptation is considered  with respect to the triplet "noise level -- noise distribution -- sparsity". These rates turn out to be different from the minimax non-adaptive rates when the triplet is known. A crucial issue is the ignorance of the noise level. Moreover, knowing or not knowing the noise distribution can also influence the rate. For example, the rates of estimation of the noise level can differ depending on whether the noise is Gaussian or sub-Gaussian without a precise knowledge of the distribution.  Estimation of noise level in our setting can be viewed as an adaptive variant of robust estimation of scale in the contamination model, where instead of fixing the "nominal" distribution in advance we assume that it belongs to some class of distributions. We also show that in the problem of estimation of a sparse vector under the $\ell_2$-risk when the variance of the noise in unknown, the optimal rate depends dramatically on the design. In particular, for noise distributions with polynomial tails, the rate can range from sub-Gaussian to polynomial depending on the properties of the design.

Feb 26

2018

Vacances

 

 

 

 

Mars 5

2018

Rajarshi Mukherjee

Berkeley

Global Testing Against Sparse Alternatives under Ising Models

Abstract: We study the effect of dependence on detecting sparse signals. In particular, we focus on global testing against sparse alternatives for the magnetizations of an Ising model and establish how the interplay between the strength and sparsity of a signal determines its detectability under various notions of dependence (i.e. the coupling constant of the Ising model). The impact of dependence is best illustrated under the Curie-Weiss model where we observe the effect of a "thermodynamic" phase transition. In particular, the critical state exhibits a subtle "blessing of dependence" phenomenon in that one can detect much weaker signals at criticality than otherwise. Furthermore, we develop a testing procedure that is broadly applicable to account for dependence and show that it is asymptotically minimax optimal under fairly general regularity conditions. This talk is based on joint work with Sumit Mukherjee and Ming Yuan.

Mars 12 2018

Pas de séminaire

 

Mars 19 2018

Yihong Wu 10h30-12h30

Yale

Polynomial method in statistical estimation : from large domain to mixture models – 1

Mars 22

2018

Yihong Wu 14h-17h

Yale

2

Mars 26

2018

Yihong Wu 10h30-12h30

Yale

 

14h00 – 17h00

 

 

3

 

 

Ecole doctorale – exposés des doctorants

 

Mars 29 2018

Yihong Wu 14h-17h

Yale

4

 

 

 

Avril 2 2018

Férié

 

April 5

2018

Angelika Rohde 14h-15h15

Freiburg Universität

 

Geometrizing rates of convergence under privacy constraints

Abstract : We study estimation of a functional $\theta(\Pr)$ of an unknown probability distribution $\Pr \in\P$ in which the original iid sample $X_1,\dots, X_n$ is kept private even from the statistician via an $\alpha$-local differential privacy constraint. Let $\omega_1$ denote the modulus of continuity of the functional $\theta$ over $\P$, with respect to total variation distance. For a large class of loss functions $l$, we prove that the privatized minimax risk is equivalent to $l(\omega_1((n\alpha^2)^{-1/2}))$ to within constants, under regularity conditions that are satisfied, in particular, if $\theta$ is linear and $\P$ is convex. Our results extend the theory developed by Donoho and Liu (1991) to the nowadays highly relevant case of privatized data. Somewhat surprisingly, the difficulty of the estimation problem in the private case is characterized by $\omega_1$, whereas, it is characterized by the Hellinger modulus of continuity if the original data $X_1,\dots, X_n$ are available. We also provide a general recipe for constructing rate optimal privatization mechanisms and illustrate the general theory in numerous examples. Our theory allows to quantify the price to be paid for local differential privacy in a large class of estimation problems.

 

April 6

2018

Cheng Mao – 14h-15h15

MIT

Breaking the n^{-1/2} barrier for permutation-based ranking models

 Abstract : The task of ranking from pairwise comparison data arises frequently in various applications, such as recommender systems, sports tournaments and social choice theory. There has been a recent surge of interest in studying permutation-based models, such as the noisy sorting model and the strong stochastic transitivity model, for ranking from pairwise comparisons. Although permutation-based ranking models are richer than traditional parametric models, a wide gap exists between the statistically optimal rate n^{-1} and the rate n^{-1/2} achieved by the state-of-the-art computationally efficient algorithms. In this talk, I will discuss new algorithms that achieve rates n^{-1} and n^{-3/4} for the noisy sorting model and the more general strong stochastic transitivity model respectively.

The talk is based on joint works with Jonathan Weed, Philippe Rigollet, Ashwin Pananjady and Martin J. Wainwright.

 

Avril 9 2018

Séminaire Parisien de Statistique - IHP

 

Avril 13 2018

Eric Kolaczyk – 14h-15h15

Boston University

Title:  Dynamic Networks with Multi-scale Temporal Structure

 

Abstract: We describe a novel method for modeling non-stationary multivariate time series, with time-varying conditional dependencies represented through dynamic networks. Our proposed approach combines traditional multi-scale modeling and network based neighborhood selection, aiming at capturing temporally local structure in the data while maintaining sparsity of the potential interactions. Our multi-scale framework is based on recursive dyadic partitioning, which recursively partitions the temporal axis into finer intervals and allows us to detect local network structural changes at varying temporal resolutions. The dynamic neighborhood selection is achieved through penalized likelihood estimation, where the penalty seeks to limit the number of neighbors used to model the data. We present theoretical and numerical results describing the performance of our method, which is motivated and illustrated using task-based magnetoencephalography (MEG) data in neuroscience.  This is joint work with Xinyu Kang and Apratim Ganguly.

 

Avril 23 2017

Vacances

 

Avril 30 2018

Pas de séminaire

 

 

 

 

May 7 2018

Pas de séminaire

 

May 14

2018

 

 

May 21 2018

 

 

May 22

2018

Mikhail Belkin

Ohia State University

 

May 24 2018

Mikhail Belkin 16h – 18h

Ohia State University

 

May 28 2018

 

 

May 29 2018

Mikhail Belkin

Ohia State University

 

May 31 2018

Mikhail Belkin 16h - 18h

Ohia State University