Research Group "Stochastic Algorithms and Nonparametric Statistics"

14.04.15

Abstract:

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21.04.15

Michael Tretyakov (University of Nottingham, UK)

Long-time numerical integration of stochastic gradient systems

Abstract:

In applications such as molecular dynamics it is of interest to compute high-dimensional integrals with respect to a known density. One of the most powerful computational approaches to such problems exploits simulation of ergodic SDEs with the required invariant density. Stochastic gradient systems (Brownian dynamics) represent a class of SDEs suitable for this task. To compute ergodic limits, one needs to simulate SDEs over a long period of time, which requires effective numerical integrators. In this talk we will demonstrate that a non-Markovian method for stochastic gradient systems introduced in [Leimkuhler, Matthews, 2013] is of 1st weak order on finite-time intervals but has second-order accuracy in computing ergodic limits. We describe the transition from the transient to the steady-state regime of this numerical method by estimating the time-dependency of the coefficients in an asymptotic expansion for the weak error, demonstrating that the convergence to 2nd order is exponentially rapid in time. We also provide numerical tests of the theory, including comparisons of the efficiencies of the Euler scheme, the 2nd order Heun method, and the non-Markovian method. The talk is based on a joint work with B. Leimkuhler and C. Matthews (Edinburgh)

28.04.15

Vladimir Spokoiny (WIAS Berlin, HU Berlin)

Some deviation bounds for random matrices with statistical applications

05.05.15

Alexandra Suvorikova (HU Berlin)

2-Wasserstein barycenter and its applications to data analysis

12.05.15

Josef Ladenbauer (TU Berlin)

Low-dimensional spike rate dynamics of coupled adaptive model neurons

Abstract:

How the properties of single neurons and their coupling give rise to different types of functionally relevant collective dynamics can be effectively studied using population activity models derived from calibrated model neurons. The activity of single neurons is well described by an integrate-and-fire model that take into account neuronal adaptation. Considering these model neurons, subject to fluctuating inputs and sparsely coupled, the stochastic network dynamics can be characterized using the Fokker-Planck equation, which leads to a model with an infinite-dimensional state space and nonstandard boundary conditions. In this talk I will present a model reduction approach that well approximates the collective spike rate dynamics by a low-dimensional ordinary differential equation. The reduced description (i) is computationally very efficient, (ii) directly links single neuron properties and network dynamics, and (iii) allows for mathematical analyses of, for example, asynchronous and rhythmic network states.

19.05.15

Lars Ruthotto (Emory University, Atlanta)

Numerical Methods for Hyperelastic Image Registration

Abstract:

Image registration is an essential task in almost all areas involving imaging techniques. The goal of image registration is to find geometrical correspondences between two or more images. Image registration is commonly phrased as a variational problem that is known to be ill-posed and thus regularization is commonly used to ensure existence of solutions and/or introduce prior knowledge about the application in mind.

This talk presents a nonlinear regularization functional based on the theory of hyperelastic materials, which overcomes limitations of the most commonly used linear elastic model. In particular, the hyperelastic regularization functional guarantees that solutions to the variational problem exist and are one-to-one correspondences between the images, which is a key concern in most applications.

The focus of this talk is on accurate and fast numerical methods for solving hyperelastic image registration problems. Further, the potential of hyperelastic schemes is demonstrated for real-life medical imaging problems.

26.05.15

Nazar Buzun (WIAS Berlin)

Multiplier bootstrap in change point detection

Abstract:

Parameters calibration task in change point detection applies bootstrap technique for variables generation with unknown distribution. The parameters are quantiles of max of random Normal variables in sequence {xi(t)}. Bootstrap procedure implies generation of series of {xi^b(t)} using weighted data resampling. Stein identity and Slepian bridge theorems reduce bootstrap quality estimation to comparison of variance matrices of {xi(t)} and {xi^b(t)}, which is the focus of this talk.

02.06.15

Pavel Dvurechensky (WIAS Berlin)

Random gradient-free methods for web page ranking model learning

Abstract:

We consider a model of web-pages ranking which is based on a Markov Chain. Ranking vector is defined as a stationary distribution of this MC. Transition probabilities are defined by pages and links features (e.g. number of clicks, time spent on a page) and some unknown parameter vector. The goal is to find this parameter vector such that the model-based ranking vector is in a good consistence with relevance to the queries defined by experts. The problem is formulated as an optimization one which is solved by bilevel algorithm. The inner one calculates approximation for the ranking vector. The outer one is a random gradient-free method with inexact oracle.

09.06.15

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16.06.15

Prof. Mikhail Malyutov (Northeastern University, Boston, USA)

SCOT modeling, training and Homogeneity testing

Abstract:Stochastic COntext Tree (abbreviated as SCOT) is m-Markov Chain (m-MC) with every state of a string independent of the symbols in its more remote past than the {\bf context} of {\bf length} determined by the preceding symbols of this state. We model and apply SCOT for statistical inference about financial, literary and seismological stationary strings in `Information processes’, vol13, No4, Vol 14, No. 3 and volume 15, No.1, available online. . SCOT construction is also used for compression under various names VLMC, VOMC, PST, CTW. Apparently, G. Bejerano (2003) made the first SCOT Statistical Likelihood comparison application to non-stationary Bioinformatics data which seems inadequate. We evaluate SCOT contexts stationary distribution iteratively in several examples; analyze several models viewed as simplified approaches to financial modeling:, evaluate their stationary distribution, entropy rate and convergence to the Brownian motion. Financial applications showed advantage of SCOT %G–%@based testing homogeneity over GARCH.

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23.06.15

>Martin Huesmann (Universität Bonn)

The geometry of multi-marginal Skorokhod embedding

Abstract:

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30.06.15

Mario Maurelli (WIAS Berlin)

A large deviation principle for mean field interacting particle SDEs, via rough paths

Abstract:

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07.07.15

John Schoenmakers (WIAS-Berlin)

Uniform approximation of the CIR process via exact simulation at random times

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14.07.15

Marcel Ladkau (Humboldt-Universität zu Berlin)

Stochastic volatility Libor modeling and efficient algorithms for optimal stopping problems

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21.07.15

Vladimir Ulyanov (Lomonosov Moscow State University)

Asymptotic analysis for nonlinear forms in random elements

Abstract:

We will consider asymptotic behaviour mainly of quadratic forms and almost quadratic forms appeared in statistics.

25.08.15

Dr. A. Naumov (Lomonosov Moscow State University)

Limit theorems for random matrices and their applications

Abstract:The study of random matrices, and in particular the properties of their eigenvalues and eigenvectors, has emerged from applications, first in data analysis and later from statistical models for heavy-nuclei atoms. Recently Random matrix theory has found its numerous application in many other areas, for example, in computational mathematics, communication theory and portfolio theory. In my talk, I will discuss the limiting laws for the eigenvalues and eigenvectors of ensembles of large n-by-n symmetric random matrices, in the asymptotic limit n tending to infinity. Global and local regimes will be considered. I will also present some applications of Random matrix theory.