# Research Group "Stochastic Algorithms and Nonparametric Statistics"

## Seminar "Modern Methods in Applied Stochastics and Nonparametric Statistics" Winter Semester 2016/2017

• Place: Weierstrass-Institute for Applied Analysis and Stochastics, Room 406 (4th floor), Mohrenstraße 39, 10117 Berlin
• Time: Tuesdays, 3:00PM - 4:00PM
11.10.16 Dr. Christian Bayer (WIAS Berlin)
Lecture room: ESH! Smoothing the payoff for efficient computation of basket option
We consider the problem of pricing basket options in a multivariate Black-Scholes or Variance-Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high-dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse-grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster than Monte Carlo or Quasi Monte Carlo methods in dimensions up to 25. (Joint work with Markus Siebenmorgen und Raul Tempone)
18.10.16 Kirill Efimov (WIAS Berlin)
Change: Starting at 4:00 pm! Adaptive weights clustering AWC
tba
25.10.16 Valeriy Avanesov (WIAS Berlin)
Bootstrap for high-dimentional online multiscale covariance matrix change-point detection
During this talk I will present a novel approach (arXiv:1610.03783 [math.ST]) for an important problem of change point detection. Specifically, we are interested in detection of an abrupt change in the covariance structure of a high-dimensional random process -- a problem, which has applications in biostatistics and econometrics. The developed approach is essentially a significance testing procedure requiring a proper choice of a critical level. To that end a non-standard bootstrap scheme is proposed and theoretically justified under mild assumptions. The idea of the proof and the simulation study will be discussed as well.
01.11.16 Dr. Pavel Dvurechensky (WIAS Berlin)
Numerical aspects of Wasserstein distance, Wasserstein barycenters, and Hellinger-Kantorovich distance
In this talk, we will consider Wasserstein and Hellinger-Kantorovich distances. The definitions of these distances are based on specific optimization problems. The goal of the talk is to present new numerical methods for solution of these optimization problems.
08.11.16 Dr. Martin Redmann (WIAS Berlin)
Dimension reduction of large scale OU processes
SPDEs with Lévy noise can be used to model chemical, physical or biological phenomena which contain uncertainties. When discretising these SPDEs in order to solve them numerically the problem might be of large order. The goal is to save computational time by replacing large scale systems by systems of low order capturing the main information of the full model. In this talk, we therefore discuss balancing related MOR techniques. We summarise already existing results and discuss recent achievements.
15.11.16 Alexandra Suvorikova (WIAS Berlin)
Non-asymptotic confidence sets in 2-Wasserstein space and their application to change point detection
In this work, we consider probabilistic setting where the probability measures are considered to be random objects. We present a procedure of construction of confidence sets for the population barycenter and discuss its application to change point detection.
22.11.16 Prof. Dr. Vladimir Spokoiny (WIAS Berlin)
Bootstrap confidence sets for spectral projectors of sample covariance
Let $$X_{1},\ldots,X_{n}$$ be i.i.d. sample in $$\R^{p}$$ with zero mean and the covariance matrix $$\Sigma$$. The problem of recovering the projector onto the eigenspace of $$Sigma$$ from these observations naturally arises in many applications. Recent technique from \cite{KoltchLounici2015} helps to study the asymptotic distribution of the distance in the Frobenius norm $$\| P_{r} - \hat{P}_{r} \|_{2}$$ between the true projector $$P_{r}$$ on the subspace of the $$r$$th eigenvalue and its empirical counterpart $$\hat{P}_{r}$$ in terms of the effective trace of $$Sigma$$. This paper offers a bootstrap procedure for building sharp confidence sets for the true projector $$P_{r}$$ from the given data. This procedure does not rely on the asymptotic distribution of $$\| P_{r} - \hat{P}_{r} \|_{2}$$ and its moments, it applies for small or moderate sample size $$n$$ and large dimension $$p$$. The main result states the validity of the proposed procedure for finite samples with an explicit error bound on the error of bootstrap approximation. This bound involves some new sharp results on Gaussian comparison and Gaussian anti-concentration in high dimension. Numeric results confirm a nice performance of the method in realistic examples.
29.11.16 Priv.-Doz. Dr. John Schoenmakers (WIAS Berlin)
Density projection schemes for McKean-Vlasov equations and explicit solutions of OU type equations
tba
06.12.16 Andzhey Koziuk (WIAS Berlin)
Operator convex functions and matrix Bernstein type inequality
tba
13.12.16 Carlos Enrique Améndola Cerón (TU Berlin)
An introduction to algebraic statistics
Algebraic Statistics is a relatively new field that has developed rapidly in recent years, using algebraic-geometric methods to provide new tools to analyze and solve statistical problems. In this talk I will give an overview of the exciting interplay between algebra and statistics, and then briefly discuss it in the context of current research on Gaussian mixtures.
20.12.16 Dr. Karsten Tabelow (WIAS Berlin)
Cancelled! MRI data models at low SNR
In this talk we elaborate the effect of low SNR on estimated parameters in models for neuroimaging data. We will present a new method for the local estimation of the noise parameter in the signal distribution and demonstrate how this can be used for improved estimation of model parameters. (joint work with Joerg Polzehl).
03.01.17 No Seminar

10.01.17 No Seminar

17.01.17 Dr. Mario Maurelli (WIAS Berlin)
A mean field SDE with Neumann boundary conditions
tba
24.01.17 Paolo Pigato (INRIA Nancy)
Statistical estimation of the oscillating Brownian motion
The Oscillating Brownian Motion is a classical, simple example of stochastic differential equation with discontinuous diffusion coefficient. It behaves like a Brownian motion which changes variance parameter each time it crosses a fixed threshold. We consider here the problem of estimating the parameters of such process from discrete observations. We propose two natural consistent estimators, which are variants of the integrated volatility estimator and take the occupation times into account. We show the stable convergence of the renormalized errors’ estimations toward some Gaussian mixture, possibly corrected by a term that depends on the local time. We then consider some applications to financial time series (in particular to volatility modeling), being the Oscillating Brownian Motion a simple way to account of volatility clustering and leverage effect. We compare our empirical results with other regime switching models. (Joint work with Antoine Lejay)
31.01.17 Maurilio Danio Gutzeit (Universität Potsdam)
Separation rates in testing if two random graphs are based on the same model
We consider two inhomogenous Erdös- Renyi graphs on the same set of vertices and study the testing problem if the random edges of these graphs have the same underlying stochastic structure. In this framework, such a structure is typically represented by a symmetric n by n matrix with entries in [0,1] and zero diagonal: entry (i,j) is the probability of edge (i,j) to occur and the edges occur independently. Now, identifying the two graphs with such matrices P and Q, respectively, we want to describe the smallest Frobenius and spectral distances between P and Q such that there is a test whose total error probability does not exceed a given level. In particular, we focus on the dependence of this distances on the number n of vertices and the number M of collected samples per graph, i.e. observed adjacency matrices. The talk will exhibit the current state of ongoing joint research with Alexandra Carpentier, Ulrike von Luxburg and Debarghya Ghoshdastidar and it will include nonasymptic results from a minimax point of view as well asymptotic (with respect to n) problem- dependent results.
07.02.17 Benjamin Stemper (WIAS Berlin)
Efficient pricing in rough Bergomi
tba
14.02.17 Dr. Karsten Tabelow (WIAS Berlin)
MRI data models at low SNR
In this talk we elaborate the effect of low SNR on estimated parameters in models for neuroimaging data. We will present a new method for the local estimation of the noise parameter in the signal distribution and demonstrate how this can be used for improved estimation of model parameters. (joint work with Joerg Polzehl).
21.02.17 Andrea Locatelli (Universität Potsdam)
Adaptation to noise parameters in non-parametric active learning
In this talk, I will present the non-parametric Active Learning classification setting already studied in Minsker (2012a) and show non-trivial strategies that can adapt to the smoothness of the regression function as well as the noise parameter and that require strictly weaker Assumptions than in previous work. We will first study the deterministic setting (i.e. one has access to the true value of the regression function) to build intuition, and then move on to the stochastic setting (noisy binary classification).
28.02.17 No Seminar due to WIAS DAY

07.03.17

14.03.17 Dr. Evgeny Burnaev (Skoltech, IITP, Moscow)
Cancelled and postponed to 28.03.17!

21.03.17 Andzhey Koziuk (WIAS Berlin)
Some ideas on Gaussian comparison and approximation
In the talk I plan to discuss new ideas and bottlenecks in the current state of research on how to upper bound Kolmogorov distance on Euclidean balls. The talk will be largely continuation of the one I gave in December 2016 and will pursue the same questions:

1. What is optimal dimensional dependence (both for comparison and approximation) of the upper-bound

2. Ways to improve Gaussian approximation

28.03.17 Dr. Evgeny Burnaev (Skoltech, IITP, Moscow)
Minimax approach to variable fidelity data interpolation
Engineering problems often involve data sources of variable fidelity with different costs of obtaining an observation. In particular, one can use both a cheap low fidelity function (e.g. a computational experiment with a CFD code) and an expensive high fidelity function (e.g. a wind tunnel experiment) to generate a data sample in order to construct a regression model of a high fidelity function. The key question in this setting is how the sizes of the high and low fidelity data samples should be selected in order to stay within a given computational budget and maximize accuracy of the regression model prior to committing resources on data acquisition. In this work we obtain minimax interpolation errors for single and variable fidelity scenarios for a multivariate Gaussian process regression. Evaluation of the minimax errors allows us to identify cases when the variable fidelity data provides better interpolation accuracy than the exclusively high fidelity data for the same computational budget. These results allow us to calculate the optimal shares of variable fidelity data samples under the given computational budget constraint. Real and synthetic data experiments suggest that using the obtained optimal shares often outperforms natural heuristics in terms of the regression accuracy.
##### References:

Gaussian Models for Data Fusion - Minimax Error of Interpolation and Optimal Design of Experiments for Variable Fidelity Data (https://goo.gl/CjgLBE) - Surrogate modeling of multifidelity data for large samples (https://goo.gl/QFkrxf)

Gaussian Process Regression and its Properties - Regression on the Basis of Nonstationary Gaussian Processes with Bayesian Regularization (https://goo.gl/haZsfM) - The Bernstein-von Mises theorem for regression based on Gaussian Processes (https://goo.gl/9whF3z) - Properties of the bayesian parameter estimation of a regression based on gaussian processes (https://goo.gl/dMd4mD)

Efficient Learning of Gaussian Process regression - Computationally Efficient Algorithm for Gaussian Process Regression in Case of Structured Samples (https://goo.gl/uXzDfW) - Adaptive Design of Experiments Based on Gaussian Processes (https://goo.gl/EjE9kt)

Surrogate Modeling for Industrial Design - GTApprox: Surrogate modeling for industrial design (https://goo.gl/mz7QtV)

04.04.17 No Seminar

11.04.17 No Seminar

18.04.17 Yangwen Sun (Humboldt-Universität zu Berlin)
tba

last reviewed: March, 27, 2017, Christine Schneider