Forschungsseminar Mathematische Statistik
Für den Bereich Statistik
A. Carpentier, S. Greven, W. Härdle, M. Reiß, V. Spokoiny
Ort
Weierstrass-Institut für Angewandte Analysis und Stochastik
Erhard-Schmidt-Raum
Mohrenstrasse 39
10117 Berlin
Zeit
mittwochs, 10.00 - 12.00 Uhr
Programm
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- 17. April 2024
- Gil Kur (ETH Zurich)
- Connections between Minimum Norm Interpolation and Local Theory of Banach Spaces
- Abstract: We investigate the statistical performance of "minimum norm'' interpolators in non-linear regression under additive Gaussian noise. Specifically, we focus on norms that satisfy either 2-uniform convexity or the cotype 2 property - these include inner-product spaces, lp norms, and Wp Sobolev spaces for 1 ≤ p ≤ 2. Our main result demonstrates that under 2-uniform convexity, the bias of the minimal norm solution is bounded by the Gaussian complexity of the class. We then prove a "reverse'' Efron-Stein type estimate for the variance of the minimal norm solution under cotype 2 - that provides an optimal bound for over-parametrized linear regression. Our approach leverages tools from the local theory of finite dimensional Banach spaces, and, to the best of our knowledge, it is the first to study non-linear models that are "far'' from Hilbert spaces.
- 24. April 2024
- Nicolas Verzelen (INRAE Montpellier)
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Computational Trade-offs in High-dimensional Clustering
- Abstract: In this talk, I will discuss the fundamental problem of clustering a mixture of isotropic Gaussian. After reviewing some results on K-means-type procedures and on some of its relaxations, I will investigate the existence of a fundamental computation-information gap for the problem of in the high-dimensional regime, where the ambient dimension p is larger than the number n of points. The existence of a computation-information gap in a specific Bayesian high-dimensional asymptotic regime has been conjectured by lesieur2016phase based on the replica heuristic from statistical physics. We provide evidence of the existence of such a gap generically in the high-dimensional regime p ≥ n, by proving a non-asymptotic low-degree polynomials computational barrier for clustering in high-dimension, matching the performance of the best known polynomial time algorithms.
- 08. Mai 2024
- Georg Keilbar, Ratmir Miftachov (Humboldt-Universität zu Berlin)
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Shapley Curves : A Smoothing Perspective
- Abstract: 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. Mai 2024
- Fabian Telschow (Humboldt-Universität zu Berlin)
- Estimation of the Expected Euler Characteristic of Excursion sets of Random fields and Applications to Simultaneous Confidence bands
- Abstract: 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. Mai 2024
- N.N. ()
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29. Mai 2024
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Tailen Hsing (University of Michigan)
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- 05. Juni 2024
- Jia-die (WIAS Berlin)
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- 12. Juni 2024
- Marc Hallin (Université libre de Bruxelles)
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- 19. Juni 2024
- N.N. ()
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- 26. Juni 2024 Achtung anderer Raum u. anderes Geb.: R. 3.13 im HVP 11a !
- Clement Berenfeld (Universität Potsdam)
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- 03. Juli 2024
- Celine Duval (Université de Lille)
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- 10. Juli 2024
- Anya Katsevich (MIT)
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- 17. Juli 2024
- N.N. ()
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Für Rückfragen wenden Sie sich bitte an:
Frau Sabine Bergmann
Mail: bergmann@mathematik.hu-berlin.de
Telefon: +49-30-2093-45450
Fax: +49-30-2093-45451
Humboldt-Universität zu Berlin
Institut für Mathematik
Unter den Linden 6
10099 Berlin, Germany