Research Group "Stochastic Algorithms and Nonparametric Statistics"

Research Seminar "Mathematical Statistics" Summer Semester 2024

  • Place: The seminar will be hybrid and realized via Zoom. Please follow the streamed talk at .
  • Time: Wednesdays, 10.00 a.m. - 12.30 p.m.
17.04.2024 Dr. Gil Kur (ETH Zürich)
Connections between minimum norm interpolation and local theory of Banach spaces
24.04.2024 Dr. Nicolas Verzelen (INRAE Montpellier)
Computational trade-offs in high-dimensional clustering
01.05.2024 Public Holiday

08.05.2024 Dr. Georg Keilbar & Ratmir Miftachov (HU Berlin)
Shapley curves: A smoothing perspective
This paper fills the limited statistical understanding of Shapley values as a variable importance measure from a nonparametric (or smoothing) perspective. We introduce population-level Shapley curves to measure the true variable importance, determined by the conditional expectation function and the distribution of covariates. Having defined the estimand, we derive minimax convergence rates and asymptotic normality under general conditions for the two leading estimation strategies. For finite sample inference, we propose a novel version of the wild bootstrap procedure tailored for capturing lower-order terms in the estimation of Shapley curves. Numerical studies confirm our theoretical findings, and an empirical application analyzes the determining factors of vehicle prices.
15.05.2024 Fabian Telschow (HU Berlin)
Estimation of the expected Euler characteristic of excursion sets of random fields and applications to simultaneous confidence bands
The expected Euler characteristic (EEC) of excursion sets of a smooth Gaussian-related random field over a compact manifold can be used to approximate the distribution of its supremum for high thresholds. Viewed as a function of the excursion threshold, the EEC of a Gaussian-related field is expressed by the Gaussian kinematic formula (GKF) as a finite sum of known functions multiplied by the Lipschitz–Killing curvatures (LKCs) of the generating Gaussian field. In the first part of this talk we present consistent estimators of the LKCs as linear projections of ''pinned" Euler characteristic (EC) curves obtained from realizations of zero-mean, unit variance Gaussian processes. As observed data seldom is Gaussian, we generalize these LKC estimators by an unusual use of the Gaussian multiplier bootstrap to obtain consistent estimates of the LKCs of Gaussian limiting fields of non-stationary statistics. In the second part, we explain applications of LKC estimation and the GKF to simultaneous familywise error rate inference, for example, by constructing simultaneous confidence bands and CoPE sets for spatial functional data over complex domains such as fMRI and climate data and discuss their benefits and drawbacks compared to other methodologies.
22.05.2024 Prof. Dr. Vladimir Spokoiny (WIAS Berlin)
Gaussian variational inference in high dimension
We consider the problem of approximating a high-dimensional distribution by a Gaussian one by minimizing the Kullback-Leibler divergence. The main result extends Katsevich and Rigollet (2023) and claims that the minimiser can be well approximated by the Gaussian distribution with the mean and variance as for the underlying measure. We also describe the accuracy of approximation and the range of applicability for such approximation in terms of efficient dimension. The obtained results can be used for analysis of various sampling scheme in optimization.
29.05.2024 Prof. Dr. Tailen Hsing (University of Michigan)
A functional-data perspective in spatial data analysis
More and more spatiotemporal data nowadays can be viewed as functional data. The first part of the talk focuses on the Argo data, which is a modern oceanography dataset that provides unprecedented global coverage of temperature and salinity measurements in the upper 2,000 meters of depth of the ocean. I will discuss a functional kriging approach to predict temperature and salinity as a smooth function of depth, as well as a co-kriging approach of predicting oxygen concentration based on temperature and salinity data. In the second part of the talk, I will give an overview on some related topics, including spectral density estimation and variable selection for functional data.
05.06.2024 Dr. Jia-Jie Zhu (WIAS Berlin)
Optimal transport and gradient flows for optimization and machine learning: Wasserstein, Hellinger, Fisher-Rao, and reproducing kernels
12.06.2024 Prof. Dr. Marc Hallin (Université Libre de Bruxelles)

19.06.2024 Evaluierung

26.06.2024 Dr. Clément Berenfeld (Universität Potsdam)
Achtung anderer Raum u. anderes Geb.: R. 3.13 im HVP 11a !
03.07.2024 Prof. Dr. Celine Duval (Université de Lille)

10.07.2024 Dr. Anya Katsevich (MIT, Cambridge, MA)


last reviewed: May 24, 2024 by Christine Schneider