Research Group "Stochastic Algorithms and Nonparametric Statistics"
Research Seminar "Mathematical Statistics" Winter Semester 2026/2027
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| 14.10.2026 | Dr. Chloé Rouyer (Universität Potsdam) |
| Derivative-free stochastic convex optimization in one dimension Stochastic convex optimization is a well understood problem when the learner has access to first-order feedback. However, when the learner can only access noisy function evaluations instead of the gradients, a logarithmic gap between upper and lower bounds has remained even in dimension one. In this talk, we will consider this problem of stochastic convex Derivative-Free Stochastic Convex Optimization in One Dimensionoptimization with zeroth-order feedback, present the tools that can be used instead of gradient and introduce a new adaptive algorithm which closes this logarithmic gap. |
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| 21.10.2026 | Prof. Dr. Kolyan Ray (Imperial College London) |
| Bayesian regression models with dense confounding variables Inferring causal relationships from observational data can be invalidated by the existence of confounding variables. We consider nonparametric Bayesian inference in regression models with additive errors under a dense confounding assumption, i.e. that every confounding variable affects many covariates. We show that by using suitable priors, which are equivalent to marginalizing out the confounders in a certain sense, such confounding can be corrected for. Our approach is illustrated via Gaussian process and spike and slab priors, for which we provide accompanying theoretical guarantees via posterior convergence rates. This is joint work with Luke Travis |
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| 28.10.2026 | Dr. Nicolas Verzelen (INRAE, Université Montpellier ) |
| Statistical-computational trade-offs: Low-degree polynomials and community recovery In many high-dimensional problems, such as planted clique, sparse PCA, clustering and community detection, the signal strength needed by the best known polynomial-time algorithms is much larger than what is information-theoretically necessary. Is this gap intrinsic? Since NP-hardness says nothing about random instances, evidence of hardness must come from other sources: average-case reductions, or lower bounds for broad classes of algorithms. In the first part, I will introduce the low-degree polynomial framework, starting from testing problems in additive models. In the Gaussian additive model, the χ² divergence and the low-degree advantage admit simple expressions in terms of the overlap between two independent copies of the signal. Comparing them shows how truncating at a low degree discards the rare large overlaps that only exhaustive search can exploit. In the second part, based on joint work with Alexandra Carpentier and Christophe Giraud, I will consider community recovery in the stochastic block model with more than ?n communities. We prove that low-degree polynomials fail below a threshold conjectured by Chin, Mossel, Sohn and Wein, for any graph density, and that this threshold lies below the Kesten?Stigum threshold. We also show that counting suitable motifs succeeds above it in moderately sparse regimes. These motifs are dictated by the lower-bound analysis: cliques, paths, and blow-ups of cycles. |
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| 04.11.2026 | Prof. Dr. Mark Podolski (Universität Luxemburg) | HVP 11 a, R.313 | Recent advances in drift estimation for high-dimensional diffusion models In this talk, we will present a selection of recent theoretical results on high-dimensional inference for the drift component of diffusion models. Such models have found numerous applications in areas including mathematical finance and biology among others. The primary focus will be on drift estimation for high-dimensional Ornstein-Uhlenbeck processes, although we will also discuss extensions to more general linear and nonlinear diffusion models. In particular, we will present Lasso-type estimators for sparse drift matrices, establish their statistical guarantees, and discuss consistent support recovery property. In the second part of the talk, we will consider drift estimation under low-rank constraints, a framework closely related to the concept of cointegration in continuous time. The presentation is based on joint work with Gabriela Ciołek, Dmytro Marushkevych, and Francisco Pina. |
| 11.11.2026 | Prof. Dr. Simon Weißmann (Universität Mannheim) |
| Stochastic optimization and regularization for inverse problems In this talk, I will investigate two perspectives on the interaction between regularization and stochastic optimization. In the first part, I will present stochastic gradient methods with decaying Tikhonov regularization and show that a suitably balanced vanishing regularization schedule can stabilize the optimization dynamics while preserving convergence to a solution of the original unregularized problem. In the second part, I will turn to data-driven variational regularization, formulated as a stochastic bilevel optimization problem. In this setting, each upper-level evaluation requires a computationally expensive and typically inexact lower-level solve. This naturally motivates the use of multilevel Monte Carlo methods, whose efficiency depends critically on the coupling between successive lower-level approximations. |
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| 18.11.2026 | Prof. Dr. Botond Szabo (Bocconi University) |
| Robust Gaussian process regression: Posterior contraction
Gaussian processes form a popular and flexible class of prior distributions with principled uncertainty quantification, but the Gaussian likelihood on which they rely makes them highly sensitive to outliers and contaminated observations. We study Gaussian process regression when among the $n$ observations, $m$ of these are possibly contaminated. A generic framework to obtain posterior contraction rates in this setting is considered, from a frequentist perspective as the sample size~$n$ and the number of corrupted observations~$m$ grow. We adopt a generalised Bayes approach in which the log--likelihood is replaced by a robustified version; we discuss various choices thereof, such as one recently proposed by Altamirano et al. (2024) that preserves conjugacy. We investigate the minimax rate of estimation under adversarial contamination in terms of the Sobolev smoothness $\be$ of the regression function and $m$. The question of building adaptive procedures to both $\be$ and $m$ is investigated, and we show that a polynomial loss for adaptation must be paid in general. We instantiate our results for Mat\'ern Gaussian process and deep ReLU network priors. Numerical experiments for existing and new robust algorithms are provided, illustrating the practical applicability of our results. |
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| 25.11.2026 | Dr. Christoph von Tycowicz (Zuse Institute Berlin, ZIB) |
| Symmetry-preserving geodesic regression on Lie Groups for longitudinal medical imaging
Many medical imaging tasks require statistical modeling of continuous transformations, including longitudinal anatomical shape change and articulated skeletal motion. These transformations naturally live on Lie groups, where meaningful statistical analysis should respect group symmetries to remain invariant to arbitrary coordinate choices and reference frames. In this talk, I will present a geodesic regression framework on Lie groups for longitudinal imaging data. Common approaches rely on Riemannian metrics, but many Lie groups do not admit a metric fully compatible with the group structure. This mismatch breaks symmetry and leads to unstable regression estimates. We therefore introduce a non-metric, bi-invariant estimator that is equivariant under both left and right group actions. We evaluate the method on synthetic data and on an open-access clinical dataset of longitudinal knee joint configurations acquired for osteoarthritis research. The proposed approach yields stable trajectories and reproducible statistical conclusions, while state-of-the-art Riemannian methods exhibit sensitivity and instability. These results highlight the practical advantages of symmetry-preserving statistical modeling in longitudinal medical imaging studies. |
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| 02.12.2026 | Dr. Hugo Cui (Laboratory of Orsay) |
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| 09.12.2026 | Prof. Dr. Yuta Koike (Tokyo University) |
| 16.12.2026 | Dr. Eardi Lila (University of Washington) |
| Geometric deep operator learning for inverse problems with functional data
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| 06.01.2027 | Prof. Dr. Claudia Strauch (Universiät Heidelberg) |
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| 13.01.2027 | |
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| 20.01.2027 | |
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| 27.01.2027 | TRR Workshop: Statistical Inference for Complex Stochastic Systems |
| HVP 11 a, R.313 |
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| 03.02.2027 | |
| 10.02.2027 | Prof. Dr. Alexander Kreiß (Universität Hildesheim) |
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| 17.02.2027 | |
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last reviewed: October 21, 2026 by Christine Schneider