# Research Seminars

## Nonparametric minimax tests for large covariance matrices - CANCELLED!

Speaker(s):
Cristina Butucea (Marne-la-Vallée)
Date:
Wednesday, June 1, 2016 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

We observe n independent p-dimensional Gaussian vectors with missing values, that is each coordinate (which is assumed standardized) is observed with probability a>0. Asymptotically, n and p tend to infinity, a tends to 0. We investigate the test problem of a simple null hypothesis that the high-dimensional covariance matrix of the underlying random vector is the identity matrix (lack of correlations).

## Uncertainty and Robustness in Stochastic Filtering

Speaker(s):
Samuel Cohen (University of Oxford)
Date:
Thursday, May 26, 2016 - 4:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

In this talk we shall consider a rigorous and systematic approach to uncertainty in problems of filtering in discrete time, using the structure of nonlinear expectations and risk measures. We shall show that, under general conditions relating the perception of uncertainty and the observation filtration, one has a forward recursion which describes the uncertainty over the current state of an unobserved process. In the setting of a discrete-time hidden Markov chain, or of the Kalman filter, we shall also obtain simple approximations which can be implemented in real time.

## Structured Semi-Definite Programming with Applications to Non-Gaussian Component Analysis

Speaker(s):
Yury Maximov (IITP RAS, Moscow)
Date:
Wednesday, May 25, 2016 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Semi-definite programming (SDP) is a popular tool for approximation of non-convex quadratic problems arises in multiple statistical and computer science problems. Known to be worst-case optimal SDP is often dominated on well-structured (practical) problems by domain specific methods and heuristics. Yet another problem of SDP is a slow computational time makes it hardly applicable for huge-scale problems. In this talk we try to incorporate problem structure in the semi-definite dual to contribute both decrease computational time and improve approximation guarantees.

## Dictionary learning: principles, algorithms, guarantee

Speaker(s):
Rémi Gribonval (INRIA Rennes)
Date:
Wednesday, May 18, 2016 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Sparse modeling has become highly popular in signal processing and machine learning, where many tasks can be expressed as under-determined linear inverse problems. Together with a growing family of low-dimensional signal models, sparse models expressed with signal dictionaries have given rise to a rich set of algorithmic principles combining provably good performance with bounded complexity. In practice, from denoising to inpainting and super-resolution, applications require choosing a “good” dictionary.

## Probabilistic Representation for Viscosity Solution of Fully nonlinear Stochastic PDEs

Speaker(s):
Anis Matoussi (Universite du Maine, Le Mans)
Date:
Thursday, May 12, 2016 - 5:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We propose a wellposedness theory for a class of second order backward doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of the solution under a Lipschitz type assumption on the generator, and we investigate the links between the 2BDSDEs and a class of parabolic fully nonlinear Stochastic PDEs. Precisely, we show that the Markovian solution of 2BDSDEs provide a probabilistic interpretation of the classical and stochastic viscosity solution of fully nonlinear SPDEs. This presentation includes some applications in pathwise stochastic control problems.

## Oracle Estimation of a Change Point in High Dimensional Quantile Regression

Speaker(s):
Simon Lee (Seoul National University)
Date:
Wednesday, May 11, 2016 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

In this paper, we consider a high dimensional quantile regression model where the sparsity structure may differ between the two sub-populations.We develop 1-penalized estimators of both regression coefficients and the threshold parameter. Our penalized estimators not only select covariates but also discriminate between a model with homogeneous sparsity and a model with a change point. As a result, it is not necessary to know or pretest whether the change point is present, or where it occurs.

## Bootstrap tuned model selection

Speaker(s):
Date:
Wednesday, May 4, 2016 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

In the problem of model selection for a given family of linear estimators \tilde{\theta}_m, m \in, ordered by their variance, we offer a new "smallest accepted" approach motivated by Lepski's device and the multiple testing idea. The procedure selects the smallest model which satisfies the acceptance rule based on comparison with all larger models.

## Asymptotic Lower Bounds for Optimal Tracking a Linear Programming Approach

Speaker(s):
Mathieu Rosenbaum (Université Pierre et Marie Curie, Paris 6)
Date:
Thursday, April 28, 2016 - 5:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We consider the problem of tracking a target whose dynamics is modeled by a continuous Ito semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be related to the time-average control problem of Brownian motion, which is characterized as a deterministic linear programming. A comprehensive list of examples with explicit expressions for the lower bounds is also provided. This is joint work with Jiatu Cai and Peter Tankov.

## Is adaptive early stopping possible in statistical inverse problems?

Speaker(s):
Gilles Blanchard (Universität Potsdam)
Markus Reiß (Humboldt-Universität zu Berlin)
Date:
Wednesday, April 27, 2016 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

We consider a standard setting of statistical inverse problem, taking the form of the Gaussian sequence model with D observed noisy coefficients. Consider the simple family of keep or kill estimators depending on a cutoff index k_0.

## Monge-Kantorovich Ranks and Signs

Speaker(s):
Marc Hallin (de L'Université libre de Bruxelles)
Date:
Wednesday, April 20, 2016 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Unlike the real line, the real space RK, K≥ 2 is not naturally" ordered. As a consequence, such fundamentals univariate concepts as quantile and distribution functions, ranks, signs, all order-related, do not straightforwardly extend to the multivariate context. Since no universal pre-existing order exists, each distribution, each data set, has to generate its own---the rankings behind sensible concepts of multivariate quantile, ranks, or signs, inherently will be distribution-specific and, in empirical situations, data-driven.