Research Group "Stochastic Algorithms and Nonparametric Statistics"

01.04.14

Valentin Patilea (INSA, Rennes, Frankreich)

Testing for lack of fit in functional regression models

08.04.14

Joscha Diehl (TU Berlin)

Stochastic partial differential equations: A rough path view

We revisit (backward) SPDE theory as classically considered by Kunita, Pardoux and others from a rough path perspective.

15.04.14

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22.04.14

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29.04.14

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06.05.14

Jens Stange (WIAS Berlin)

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13.05.14

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20.05.14

Thorsten Dickhaus (WIAS Berlin)

Control of the false discovery rate under positive dependency

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27.05.14

Lars Ruthotto (University of British Columbia, Vancouver)

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 from Positron Emission Tomography (PET), Diffusion Tensor Imaging (DTI), and Dynamic Contrast Enhanced MRI (DCE-MRI).

03.06.14

Pavel Dvurechenskii (Moscow Institute of Physics and Technology, Russia)

Gradient methods for convex problems with stochastic inexact oracle

Abstract: The first goal of the talk is to familiarize listeners with recent results by Olivier Devolder, Francois Glineur, and Yurii Nesterov concerning convex optimization problems with inexact oracle. Two levels of inexactness are considered: a deterministic one, which means that the function is convex and approximately smooth; and stochastic one, which means that we are alowed to calculate only stochastic approximation of the function value and gradient. In his PhD thesis O. Devolder showed that dual gradient method for such problems has slow convergence rate but doesn't accumulate the error of the oracle. On the contrary the fast gradient method has faster convergence rate but linearly accumulates the oracle error. O. Devolder proposed an intermediate gradient method (IGM) for inexact oracle. This method allows to play with tradeoff between the speed and error accumulation depending on the problem parameters. The second goal of the talk is to present a new IGM which can be applied to the problems with composite structure, stochastic inexact oracle and non-euclidean setup. Joint work with Alexander Gasnikov.

10.06.14

Tigran Nagapetyan (WIAS Berlin)

Multi-level Monte Carlo for Approximation of Distribution Functions and an Application to AF4

Abstract: The multi-level Monte Carlo approach is a powerful variance reduction technique, which is applied, in particular, in the context of stochastic differential equations. While the standard task is to compute the expectation of a real-valued functional on the path space, in this talk we discuss how to approximate its distribution function or density on a compact interval in this talk. We illustrate the basic idea of multi-level Monte Carlo, and we establish upper bounds for the error of suitable algorithms. Moreover, we briefly discuss an application to asymmetric flow field flow fractionation (AF4), which is a process engineering technique for the separation of nanoparticles.

17.06.14

Peter Mathé (WIAS Berlin)

Overcoming saturation in Bayesian inverse problems

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24.06.14

Name:Juho Haeppoelae (KAUST)

Titel:Weak approximation of SDE by a mean square error adaptive multilevel Monte Carlo method

Abstract:We present a multilevel Monte Carlo (MLMC) method for weak approximation of stochastic di%Gff%@erential equations (SDE) that uses an a posteriori strong error adaptive Euler%G–%@Maruyama step-size control in the numerical integration of SDE realizations. Strong error adaptivity turns out to be useful for weak approximation MLMC methods since it provides a reliable and e%Gffi%@cient way to control the statistical error of the weak approximation MLMC estimator. For a large set of low-regularity weak approximation problems the adaptive Euler%G–%@Maruyama method produces an approximation to a predescribed accuracy with a lower asymptotic cost than what typically can be obtained by the uniform time-step Euler%G–%@Maruyama MLMC method on the given set of problems. The cost reduction is illustrated in numerical studies of a 1D and a higher dimensional low-regularity weak approximation problem.

01.07.14

Name: Pavel Dvurechenskii (Moskau)

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08.07.14

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18.08.14

Name:Prof. Alexander Veretennikov (University of Leeds, UK)

Titel: On local mixing conditions for degenerate SDEs

Abstract: In studying ergodic properties of SDEs such as convergence rates to stationary regimes, two major tools are frequently in use: recurrence and local mixing. This talk is devoted mainly to the latter. Beside the simple ``petite sets'' condition, there is a more effective and natural option called Markov-Dobrushin's condition. This condition will be discussed for Ito's SDEs. It will be shown how to verify this condition for non-degenerate, degenerate and highly degenerate equations, in particular with some non-regular drift coefficients. Note that both degeneracy and the lack of regularity prevent from using easily the ``petite sets''; however, Markov-Dobrushin's condition works well.