Forschungsgruppe "Stochastische Algorithmen und Nichtparametrische Statistik"
Research Seminar "Mathematical Statistics" Winter Semester 2023/24
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| 18.10.2023 | N.N. |
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| 25.10.2023 | Prof. Dr. Denis Belomestny (Universität Duisburg-Essen) |
| Provable benefits of policy learning from human preferences A crucial task in reinforcement learning (RL) is a reward construction. It is common in practice that no obvious choice of reward function exists. Thus, a popular approach is to introduce human feedback during training and leverage such feedback to learn a reward function. Among all policy learning methods that use human feedback, preference-based methods have demonstrated substantial success in recent empirical applications such as InstructGPT. In this work, we develop a theory that provably shows the benefits of preference-based methods in tabular and linear MDPs. The main idea of our method is to use KL-regularization with respect to the learned policy to ensure more stable learning. |
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| 01.11.2023 | Prof. Dr. Victor Panaretos (EPFL Lausanne) |
| Optimal transport for covariance operators Covariance operators are fundamental in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loève expansion. These operators may themselves be subject to variation, for instance in contexts where multiple functional populations are to be compared. Statistical techniques to analyse such variation are intimately linked with the choice of metric on covariance operators, and the intrinsic infinite-dimensionality and of these operators. I will describe how the geometry and tools of optimal transportation can be leveraged to construct natural and effective statistical summaries and inference tools for covariance operators, taking full advantage of the nature of their ambient space. Based on joint work with Valentina Masarotto (Leiden), Leonardo Santoro (EPFL), and Yoav Zemel (EPFL). |
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| 08.11.2023 | Dr. Sven Wang (Humboldt-Universität zu Berlin) | Statistical convergence rates for transport- and ODE-based generative models Measure transport provides a powerful toolbox for estimation and generative modelling of complicated probability distributions. The common principle is to learn a transport map which couples a tractable (e.g. uniform or normal) reference distribution to some complicated target distribution, e.g. by maximizing a likelihood objective. In this talk, we discuss recent advances in statistical convergence guarantees for such methods. While a general theory is developed, we will primarily treat (1) triangular maps which are the building blocks for "autoregressive normalizing flows" and (2) ODE-based maps, defined through an ODE flow. The latter encompasses NeuralODEs, a popular method for generative modeling. Our results imply that transport methods achieve minimax-optimal convergence rates for non-parametric density estimation over Hölder classes on the unit cube. Joint work with Youssef Marzouk (MIT, United States), Robert Ren (MIT, United States) and Jakob Zech (U Heidelberg, Germany). |
| 15.11.2023 | N. N. |
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| 22.11.2023 | Prof. Dr. Marc Hoffmann (Université Paris-Dauphine) |
| Achtung anderer Raum: 406, 4. OG ! | On estimating multidimensional diffusions from discrete data
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| 29.11.2023 | Prof. Dr. Martin Spindler (Universität Hamburg) |
| Achtung anderer Raum u. anderes Geb.: R. 3.13 im HVP 11a ! | High-dimensional L2-boosting: Rate of convergence (hybrid talk) |
| 06.12.2023 | N.N. |
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| 13.12.2023 | Dr. Boris Buchmann (ANU Canberra, Australia) |
| Weak subordination of multivariate Levy processes Subordination is the operation which evaluates a Levy process at a subordinator, giving rise to a pathwise construction of a "time-changed" process. In probability semigroups, subordination was applied to create the variance gamma process, which is prominently used in financial modelling. However, subordination may not produce a levy process unless the subordinate has independent components or the subordinate has indistinguishable components. We introduce a new operation known as weak subordination that always produces a Levy process by assigning the distribution of the subordinate conditional on the value of the subordinator, and matches traditional subordination in law in the cases above. Weak subordination is applied to extend the class of variance-generalised gamma convolutions and to construct the weak variance-alpha-gamma process. The latter process exhibits a wider range of dependence than using traditional subordination. Joint work with Kevin W. LU - Australian National University (Australia) & Dilip B. Madan - University of Maryland (USA) |
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| Freitag, 15.12.2023 | Prof. Dr. Laura Sangalli (MOX Milano, Italien) |
| An additional session! | Physics-informed spatial and functional data analysis
Recent years have seen an explosive growth in the recording of increasingly complex and high-dimensional data, whose analysis calls for the definition of new methods, merging ideas and approaches from statistics and applied mathematics. My talk will focus on spatial and functional data observed over non-Euclidean domains, such as linear networks, two-dimensional manifolds and non-convex volumes. I will present an innovative class of methods, based on regularizing terms involving Partial Differential Equations (PDEs), defined over the complex domains being considered. These Physics-Informed statistical learning methods enable the inclusion of the available problem specific information, suitably encoded in the regularizing PDE. Illustrative applications from environmental and life sciences will be presented. |
| 20.12.2023 | N.N. |
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| 10.01.2024 | Prof. Dr. Eric Moulines (Ecole Polytechnique) |
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| 17.01.2024 | |
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| 24.01.2024 | Simon Wood (University of Edinburgh) |
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| 31.01.2024 | |
| Achtung anderer Raum: 406, 4. OG ! |
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| 07.02.2024 | |
| 14.02.2024 | |
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last reviewed: October 16, 2023 by Christine Schneider