Research Group "Stochastic Algorithms and Nonparametric Statistics"
Seminar "Modern Methods in Applied Stochastics and Nonparametric Statistics" Summer Semester 2018
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| 17.04.2018 | Prof. Peter Friz (WIAS und TU Berlin) |
| Algebraic statistics meets rough paths, joint work with C. Armendola and B. Sturmfels The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is here examined through the lens of algebraic geometry. We introduce varieties of signature tensors for both deterministic and random paths. For the former, we focus on piecewise linear paths, on polynomial paths, and on varieties derived from free nilpotent Lie groups. For the latter, we focus on Brownian motion and its mixtures. |
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| 24.04.2018 | No Seminar |
| 01.05.18 | Public holiday |
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| 08.05.18 | Dr. Valeriy Avanesov (WIAS Berlin) |
| SDE's, Gaussian Processes, Clusters, etc. |
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| 15.05.18 | Dr. Michele Coghi (WIAS Berlin) |
| Interacting Particle Systems |
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| 22.05.18 | Dr. Tobias Kley (Humboldt-Universität zu Berlin) |
| Sequential detection of structural changes in irregularly observed data Online surveillance of time series is traditionally done with the aim to identify changes in the marginal distribution under the assumption that the data between change-points is stationary and that new data is observed at constant frequency. In many situations of interest to data analysts, the classical approach is too restrictive to be used unmodified. We propose a unified system for the monitoring of structural changes in streams of data where we use generalised likelihood ratio-type statistics in the sequential testing problem, obtaining the flexibility to account for the various types of changes that are practically relevant (such as, for example, changes in the trend of the mean). The method is applicable to sequences where new observations are allowed to arrive irregularly. Early identification of changes in the trend of financial data can assist to make trading more profitably. In an empirical illustration we apply the procedure to intra-day prices of components of the NASDAQ-100 stock market index. This project is joint work with Piotr Fryzlewicz. |
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| 29.05.18 | No Seminar |
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| 05.06.18 | Priv.-Doz. Dr. Peter Mathé: |
| Nyström subsampling for regression functions of low smoothness |
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| 12.06.18 | Dr. Pavel Dvurechensky (WIAS Berlin) |
| Distributed calculation of Wasserstein barycenters We study the semi-discrete optimal transport problem of decentralized distributed computation of a discrete approximation for regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. Particularly, we assume that there is a network of agents/machines/computers where each agent holds a private continuous probability measure, and seek to compute the barycenter of all the measures in the network by getting samples from its local measure and exchanging information with its neighbors. Motivated by this problem, we develop a novel accelerated primal-dual stochastic gradient descent method for general stochastic convex optimization problems with linear equality constraints, and modify it for decentralized distributed optimization setting to generate a new algorithm for the distributed semi-discrete regularized Wasserstein barycenter problem. The proposed algorithm can be executed over arbitrary networks that are undirected, connected and static, using the local information only. Moreover, we show explicit non-asymptotic convergence rates in terms of the problem parameters. Finally, we show the effectiveness of our method on the distributed computation of the regularized Wasserstein barycenter of univariate Gaussian and von Mises distributions; as well as some applications to image aggregation. |
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| 19.06.18 | Prof. Zuoqiang Shi (Tsinghua University) |
| Low dimensional manifold model for image processing In this talk, I will introduce a novel low dimensional manifold model for image processing problem. This model is based on the observation that for many natural images, the patch manifold usually has low dimension structure. Then, we use the dimension of the patch manifold as a regularization to recover the original image. Using some formula in differential geometry, this problem is reduced to solve Laplace-Beltrami equation on manifold. The Laplace-Beltrami equation is solved by the point integral method. Numerical tests show that this method gives very good results in image inpainting, denoising and super-resolution problem. This is joint work with Stanley Osher and Wei Zhu. |
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| 26.06.18 | Dr. Alexandra Suvorikova (WIAS Berlin) |
| CLT in 2-Wasserstein space |
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| 03.07.18 | Dr. Paolo Pigato (WIAS Berlin) |
| Asymptotic analysis of rough volatility models |
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| 10.07.18 | |
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| 17.07.18 | |
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| 24.07.18 | |
last reviewed: May 14 , 2018, Christine Schneider