Research Group "Stochastic Algorithms and Nonparametric Statistics"

Seminar "Modern Methods in Applied Stochastics and Nonparametric Statistics" Summer Semester 2017

  • Place: Weierstrass-Institute for Applied Analysis and Stochastics, Room 406 (4th floor), Mohrenstraße 39, 10117 Berlin
  • Time: Tuesdays, 3:00PM - 4:00PM
18.04.17 Yangwen Sun (Humboldt-Universität zu Berlin)
Minimum spanning tree approach for change-point detection
Change-point detection has been demonstrated to be useful in various areas. As the dimension and size of the data increase , the detection of the change-point becomes more challenging. A recent graph-based approach by Chen and Zhang (2015) has claimed to be effective especially in the high dimensional case. In this talk, we will focus on an approach based on minimum spanning tree (MST) graph. The change-point detection problem is characterized as a test of a significant change in the probability distribution. The proposed MST-based dissimilarity measure, the selection of critical level for the test, and the performance of the approach will be presented in this talk.
25.04.17 Nikita Zhivotovskiy (IITP RAS, SkolTech)
Towards minimax optimal rates in classification and regression
In this talk, we consider two approaches that allow (in some cases) to obtain minimax rates of the prediction risk up to absolute constants. Classification problems will be considered under small noise conditions for an arbitrary distribution of objects, as well as cases of certain special distributions. In contrast to several standard results in the learning theory, our bounds are simultaneously optimal for entire families of classes.
02.05.17 Alexey Kroshnin (Moscow Institute of Physics and Technology, IITP RAS)
Fréchet Barycenters in the Monge-Kantorovich spaces
Let P(X) be a space of probability measures on an arbitrary Polish space X. We will discuss a Monge—Kantorovich distance with an arbitrary cost function, given as a solution of optimal transportation problem between two measures from P(X). A useful property of this distance is that it takes into account the geometry of underlying space X. We will show that for a wide class of cost functions the Monge—Kantorovich distance generates a topology on P(X) and consider the properties of this space. Furthermore, we will introduce the notion of Fréchet barycenter which is a generalization of Wasserstein barycenters. It will be shown that the Fréchet barycenters have some regular properties, e.g. they are continuous, consistent etc.
09.05.17 Prof. Andrey Sobolevskiy (IITP, Russian Academy of Sciences, Moscow)
The Hamilton-Jacobi equation: Parallel transport in the 2-Wasserstein space and beyond
The Hamilton-Jacobi equation with quadratic Hamiltonian describes parallel transport in the 2-Wasserstein space of measures. While geodesics in Wasserstein spaces arise as solutions to two-point boundary value problem, the natural setting for the Hamilton-Jacobi equation is an initial value problem. We will describe the corresponding dynamics for measures, first constructed by Ilya Bogaevski for the quadratic Hamiltonian, and its extension to a general convex Hamiltonian due to Konstantin Khanin and the speaker.

23.05.17 Prof. Archil Gulisashvili (Ohio University, USA)
Extreme-strike asymptotics for general Gaussian stochastic volatility














last reviewed: April, 21, 2017, Christine Schneider