# 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. 16.05.17 23.05.17 Prof. Archil Gulisashvili (Ohio University, USA) Extreme-strike asymptotics for general Gaussian stochastic volatility 30.05.16 Paul Fischer (Humboldt-Universität zu Berlin) The talk takes place at ESH ! Overview of the paper "Estimating the cluster tree of a density by analyzing the minimal spanning tree of a sample" by Werner Stuetzle 06.06.17 Dr. Martin Eigel (WIAS Berlin) Sampling-free solution of stochastic forward and inverse problems We consider two typical problem classes of UQ: PDEs with random data and Bayesian inversion for these random models. Opposite to classical stochastic approaches, spectral (functional) methods allow for a sampling-free explicit evaluation of probability densities. The formulation is amenable to modern model reduction techniques such as hierarchical tensor approximations and allows for an adaptive error control. 13.06.17 Alexandra Suvorikova (WIAS Berlin) The talk takes place at HVP 11 a, room 4.13! Detection of structural breaks in complex data In this talk we discuss two approaches to detection of structural breaks in complex data. We focus on the online mode, where a structural break in a running stochastic process should be detected as soon as possible under constraint on a given in advance false-alarm rate. We exploit a framework, that is common for the solution of problems of this type, namely the hypothesis testing in a scrolling window. The first approach relies on the quasi likelihood-ratio test. The second part of the present work considers the case, when observed data set comes from a space of probability measures with finite second moments endowed with 2 -Wasserstein distance. 20.06.17 Gloria Xiao (Humboldt-Universität Berlin) A review of the paper "A Tutorial on Spectral Clustering" by Ulrike von Luxburg 27.06.17 Cassandra Uebel (Humboldt-Universität Berlin) Variable selection with hamming loss 04.07.17 Prof Lars Ruthotto (Emory University, Atlanta) Stable architectures for deep neural networks 11.07.17 Chiheb Ben Hammouda (KAUST, Saudi Arabia) Multilevel hybrid split-step implicit tau-leap In biochemically reactive systems with small copy numbers of one or more reactant molecules, the dynamics is dominated by stochastic effects. To approximate those systems, discrete state-space and stochastic simulation approaches have been shown to be more relevant than continuous state-space and deterministic ones. In systems characterized by having simultaneously fast and slow timescales, existing discrete space-state stochastic path simulation methods, such as the stochastic simulation algorithm (SSA) and the explicit tau-leap (explicit-TL) method, can be very slow. Implicit approximations have been developed to improve numerical stability and provide efficient simulation algorithms for those systems. Tn this talk, we propose an efficient Multilevel Monte Carlo (MLMC) method in the spirit of the work by Anderson and Higham (SIAM Multiscal Model. Simul. 10(1), 2012). This method uses split-step implicit tau-leap (SSI-TL) at levels where the explicit-TL method is not applicable due to numerical stability issues. We present numerical examples that illustrate the performance of the proposed method. 18.07.17 Dr. Mario Maurelli (WIAS Berlin) 2D Stochastic Euler equations: Flow representation and vortex approximation We consider two dimensional Euler equations (in vorticity form) for incompressible fluids, with a stochastic term of transport-type. Deterministic Euler equations in 2D can be associated with an ODE with non-local (mean field) way. We extend this interpretation to the stochastic case and we provide well-posedness and suitable particle approximation. This is based on joint works with Michele Coghi, Franco Flandoli and Zdzislaw Brzezniak. 25.07.17 Benjamin Stemper (WIAS Berlin) Some thoughts on calibration under rough volatility via deep learning 01.08.17 Andzhey Koziuk (WIAS Berlin) Smooth representation of the Kolmogorov distance In this talk, we consider several types of accelerated randomized gradient methods: random directional search, random coordinate descent, randomized zero-order method. Using the concept of inexact oracle, we present a generic theorem on the convergence rate for all the three methods. Despite their random nature, these methods have complexity with the same dependence on the desired accuracy of the solution as deterministic accelerated gradient method. Joint work with A. Gasnikov 08.08.17 no seminar tba 15.08.17 no seminar 22.08.17 no seminar 29.08.17 Alexander Zadorozhnyi (Universität Potsdam) Concentration of weakly dependent Banach-valued sums and applications to kernel learning methods We obtain a new Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate statistical rates of convergence for the broad family of spectral regularization methods for reproducing kernel decision rules, when trained on a sample coming from a stationary $\tau-$mixing process. 05.09.17

last reviewed: August, 17, 2017, Christine Schneider