Research Group "Stochastic Algorithms and Nonparametric Statistics"

12.04.16

Johannes Ebert (Humboldt-Universität zu Berlin)

Wasserstein barycenters of random probability measures

Abstract:

19.04.16

Dr. Roland Hildebrand (WIAS Berlin)

Regression based duality approach to optimal control with application to hydro electricity storage

Abstract: We present ongoing research on optimal control of a cascade of hydro-electricity production facilities coupled with a model of the day-by-day electricity bid market. We consider different aspects of the dual martingale approach used to tackle this problem.

26.04.16

Dr. P. Dvurechenski (WIAS Berlin)

Gradient and gradient-free methods for learning a web-page ranking algorithm

Abstract: In this talk we consider a web page ranking model based on markov chain.. Transition probabilities in this model depend on unknown parameters which are to be found using experts information about pages relevance to a user query. The learning problem is stated as an optimization problem. We discuss two approaches for solution of this problem: random gradient-free and full gradient. We study rate of convergence and memory amount which is needed for the proposed algorithms. The talk is based on a joint work https://arxiv.org/abs/1603.00717 with L. Bogolubsky, A. Gasnikov, G. Gusev, Y. Nesterov, A. Raigorodskii, A. Tikhonov, M. Zhukovskii

03.05.16

On Entropy-Transport problems and the Hellinger-Kantorovich distance

In this talk, we discuss a general class of variational problems involving entropy-transport minimization with respect to a couple of given finite measures with possibly different total mass. Problems of this kind are a natural generalization of classical optimal transportation problems. For certain choices of the entropy/cost functionals they provide a family of distances between measures, that lie between the Hellinger and the Kantorovich-Wasserstein ones and have interesting geometric properties. The connection to the original entropy/transport problem relies on convex duality in a surprising way. A suitable dynamic Benamou-Brenier characterization also shows the link of these distances to dynamic processes of gradient-flow type.

10.05.16

Prof. Leonid Berlyand (Pennsylvania State University)

Phase field model of cell motility: Sharp interface limit and traveling waves

Abstract:Phase field models are very ecient in computational studies of moving deformable in- terfaces. We will present a phase field system that models the motion of a eukaryotic cell on a substrate and investigate the dependence of this motion on key physical parameters. This system consists of two PDEs: the Allen-Cahn equation for the scalar phase eld function coupled with a vectorial parabolic equation for the orientation of the actin lament network. Two key features of this system are (i) the gradients coupling and (ii) volume preservation constraints. We pass to the sharp interface limit (SIL), which reduces the system to a single scalar equation and show that the motion of the cell boundary is the mean curvature motion modied by a novel nonlinear term. Numerical and analytical studies of the SIL equation reveal the existence of two distinct regimes of the physical parameters. The subcritical regime was studied numerically and analytically by my Ph. D. student M. Mizuhara. Our main focus is the supercritical regime. Here we established surprising features of the motion of the interface such as discontinuities of velocities, hysteresis in the 1D model, instability of the circular shape, rise of asymmetry in the 2D model, and existence of non-trivial traveling waves. Because of features (i)-(ii), classical comparison principle techniques do not apply to this system. Furthermore, the system can not be written in a form of gradient ow, which is why ô-convergence techniques also can not be used. Instead, our derivation of SIL is based on a special asymptotic ansatz. This is joint work with V. Rybalko and M. Potomkin.

17.05.16

Dr. Peter Mathé (WIAS Berlin)

Bayes methods within the BOP project

Abstract: Within the BOP project the fundamental BOP solver is enhanced by several features which rely on statistical techniques. We review some contributions with particular emphasis on Bayesian methods for model calibration. We will discuss a full nonlinear Bayes using Markov chain Monte Carlo, and a local linear Bayes which is known as Gaussian process regression.

24.05.16

Dr. Olaf Klein (WIAS Berlin)

The play-operator, the Preisach-operator and its variants: Identification and evaluation

Abstract: An important tool to model hysteresis effects like magnetization or plasticity or memory in markets are the so-called hysteresis operators. In this talk, two important operators will be introduced: the play operator and the Preisach operator. The identification of the weight function in the Preisach operator from the so-called Everett function will be discussed. Also the determination of the Everett function from measured so-called First Order Reversal curves (FORCs) will be considered.

31.05.16

Andrea Locatelli (Universitäat Potsdam)

Pure exploration bandit problems

Abstract: In this talk, we will present the classical multi-armed bandit problem and its pure exploration variant. We will then focus on a new lower bound for the Best Arm Identification problem, and introduce a new pure exploration problem: the thresholding bandit problem, for which we will show a lower bound and a novel algorithm to solve this problem .

07.06.16

Dr. Alexey Naumov (Lomonosov Moscow State University)

Extreme singular values of random matrices

Abstract:In my talk I will discuss the bounds for the smallest and largest singular values of different random matrix ensembles. These bounds play a crucial role in many limit theorems in Random matrix theory. Some applications to numerical mathematics and data analysis will be given as well. The talk will be partially based on joint results with F. G\"otze and A. Tikhomirov.

14.06.16

Dr. Fabian Dickmann (WIAS Berlin)

Deloitte-WIAS Project: Multi-curve LIBOR model and calibration to caps and swaptions

Abstract: Since the financial crisis, the LIBOR rates are no longer considered safe. In particular, the longer the LIBOR period, the larger the risk. This has led to the problem of so called multiple curve LIBOR modeling. In this setting, we introduce a multiple curve framework that combines a Libor Market Model and a riskless Overnight Indexed Swap (OIS) rate. The spread between those two, called "basis spread", must be taken into account when pricing financial derivatives. In cooperation with Deloitte and Touche, appropriate models are developed and implemented.Moreover, we develop a calibration procedure that allows for matching real market data to prices of different standard LIBOR derivatives.

21.06.16

Maurilio Danio Gutzeit (Universität Potsdam)

Minimax separation rates for testing convex hypotheses in ^{R^d}

Abstract:We consider composite- composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a convex subset C of ^{R^d} . We adopt a minimax point of view and our primary objective is to describe the smallest Euclidean distance between the null and alternative hypotheses such that some test can attain a given power. In particular, we focus on the dependence of this distance on the dimension d and the sample size/ variance parameter n giving rise to the minimax separation rate. In this talk we will discuss lower and/ or upper bounds on this rate for different smooth and non- smooth choices for C. (Based on ongoing joint research with Alexandra Carpentier and Gilles Blanchard.)

28.06.16

Dr.. Artem Sapozhnikov (MPI MIS, Leipzig)

Geometric aspects of random walks on large tori

Abstract:In this talk, we consider the fragmentation of a discrete d-dimensional torus (d>=3) by a simple random walk, a basic mathematical model for the gel degradation by an enzyme. We overview recent results and open problems about geometric properties of the random walk trace and its complement on relevant time scales.

05.07.16

Dr. Joaquim Serra (WIAS Berlin)

American option pricing with Lévy diffusion: an introduction to nonlocal equations

Abstract: In the last decade, there has been an explosion of papers studying nonlocal equations within the PDE community. Some of the main applied motivations come from mathematical finance. Many outstanding mathematicians have updated the old PDE tools, and developed new ones when necessary, in order to study in depth nonlinear elliptic and parabolic nonlocal equations. In this talk, I would like to present, from a very broad perspective, some recent results in collaboration with L. Caffarelli and X. Ros-Oton on the optimal regularity of the solutions and the regularity of the free boundaries (near regular points) for nonlocal obstacle problems. These problems arise in pricing of American options under non-Gaussian diffusion of the underlying stock price. The talk will be oriented to a broad audience with expertise and interest in modeling and not necessarily in regularity theory.. The previous research results will serve more as a context rather that being the main goal of the talk. I would like to introduce the basics on nonlocal equations, and to briefly explain its theoretical interest ---also discussing with the audience its applied interest. Last, I would like to discuss with the audience, in a very open way, what are the best current models (arising from data analysis) for option pricing. The true goal of the talk will be to raise the following (very ambitious perhaps) question: What is The Equation to be studied, now that we have very flexible methods?

12.07.16

Abstract:

19.07.16

Sebastian Boeckel (Humboldt-Universität zu Berlin)

High-dimensional nonparametric hypothesis testing using Monge-Kantorovich-depth

Abstract:How to talk about quantiles, ranks and signs of a measure in R^d with d>1? Monge-Kantorovich-depth is a proposal for the generalization of these concepts to higher dimensions. It is proposed to evaluate the optimal transport map (wrt. to quadratic risk) of the measure into the uniform distribution of the unit ball. It can be shown, that these notions specialize to their usual counterparts in d=1 and for elliptic families and that it can be empirically evaluated. As an application it is proposed to test nonparametric hypothesis in a high-dimensional setting.

23.08.16

Prof. Alexander Goldenschluger (University of Haifa)

Statistical inference for the M/G/infinity queue

Abstract:The subject of this talk is statistical inference on the service time distribution and its functionals in the M/G/infty queue from incomplete data. We consider two observation settings and discuss different approaches to constructing estimators. We develop estimators of the service time distributions and derive exact non--asymptotic bounds on their mean squared errors. The problem of estimating the service time expectation is addressed as well. We present some results on comparison of different estimators of the service time distribution.