Research Group "Stochastic Algorithms and Nonparametric Statistics"

Research Seminar "Mathematical Statistics" Summer Semester 2017

  • Place: Weierstrass-Institute for Applied Analysis and Stochastics, Erhard-Schmidt-Hörsaal, Mohrenstraße 39, 10117 Berlin
  • Time: >Wednesdays, 10.00 a.m. - 12.30 p.m.

26.04.17 Jonathan Weed (Massachusetts Institute of Technology, USA)
Optimal rates of estimation for the multi-reference alignment problem
How should one estimate a signal, given only access to noisy versions of the signal corrupted by unknown circular shifts? This simple problem has surprisingly broad applications, in fields from structural biology to aircraft radar imaging. We describe how this model can be viewed as a multivariate Gaussian mixture model whose centers belong to an orbit of a group of orthogonal transformations. This enables us to derive matching lower and upper bounds for the optimal rate of statistical estimation for the underlying signal. These bounds show a striking dependence on the signal-to-noise ratio of the problem. Joint work with Afonso Bandeira and Philippe Rigollet.

10.05.17 Prof. Marco Cuturi (ENSAE/CREST, Malakoff, France)
A review of regularized optimal transport and applications to Wasserstein barycenters


The talk takes place in R.406

14.06.17 Prof. Jean-Michel Loubes (Université Toulouse III, France)
Kantorovich distance based kernel for Gaussian Processes : estimation and forecast
Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. Here, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provide a family of positive definite kernels built using transportation based distances. We provide a probabilistic understanding of these kernels and characterize the corresponding stochastic processes. We prove that the Gaussian processes indexed by distributions corresponding to these kernels can be efficiently forecast, opening new perspectives in Gaussian process modeling.




last reviewed: march 3, 2017, by Christine Schneider