Studierende und Gäste sind jederzeit herzlich willkommen. Wenn nicht explizit anders unten angegeben, finden alle Vorträge in Präsenz im Raum 2.059 statt. Für die Aufnahme in den E-Mail-Verteiler für die Einladungen kontaktieren Sie bitte Tatjana Dominic (firstname.lastname@example.org).
|20.30 SR 2.59
|Prof. Dr. Nicole Bäuerle
|Sprechstunde: nach Vereinbarung.
|Zimmer 2.016 Kollegiengebäude Mathematik (20.30)
|Prof. Dr. Vicky Fasen-Hartmann
|Sprechstunde: Nach Vereinbarung.
|Zimmer 2.053 Kollegiengebäude Mathematik (20.30)
|Prof. Dr. Tilmann Gneiting
|Sprechstunde: nach Vereinbarung
|Zimmer 2.019 Kollegiengebäude Mathematik (20.30)
|Prof. Dr. Daniel Hug
|Sprechstunde: Nach Vereinbarung.
|Zimmer 2.051 Kollegiengebäude Mathematik (20.30)
|Prof. Dr. Günter Last
|Sprechstunde: nach Vereinbarung.
|Zimmer 2.001, Sekretariat 2.056 Kollegiengebäude Mathematik (20.30)
|Prof. Dr. Mathias Trabs
|Sprechstunde: Sprechzeit nach Vereinbarung
|Zimmer 2.020 Kollegiengebäude Mathematik (20.30)
Dienstag, 13.02.2023, 15.45 Uhr, Ort: SR 1.059
Prof. Dr. Sophie Langer (University of Twente)
The Role of Statistical Theory in Understanding Deep Learning
Abstract: In recent years, there has been a surge of interest across different research areas to improve the theoretical understanding of deep learning. A very promising approach is the statistical one, which interprets deep learning as a nonlinear or nonparametric generalization of existing statistical models. For instance, a simple fully connected neural network is equivalent to a recursive generalized linear model with a hierarchical structure. Given this connection, many papers in recent years derived convergence rates of neural networks in a nonparametric regression or classification setting. Nevertheless, phenomena like overparameterization seem to contradict the statistical principle of bias-variance trade-off. Therefore, deep learning cannot only be explained by existing techniques of mathematical statistics but also requires a radical overthinking. In this talk we will explore both, the importance of statistics for the understanding of deep learning, as well as its limitations, i.e., the necessity to connect with other research areas.
Dienstag, 16.01.2024, 15.45 Uhr, Ort: SR 1.059
Maximilian Steffen (Institut für Stochastik, KIT)
Multivariate estimation in nonparametric models: Stochastic neural networks and Lévy processes
Abstract: Nowadays, statistical problems characterized by large sample sizes and large parameter spaces are ubiquitous. Moreover, a lot of training methods, while strong in practice, cannot statistically guarantee their performance in terms of risk bounds. As a consequence, the design of cutting edge methods is characterized by a tension between numerically feasible and efficient algorithms, and approaches which also satisfy theoretically justified statistical properties. In this talk, we consider two fairly disjoint problems showcasing the wide spectrum of fields where nonparametric statistics can provide answers to the challenges presented by modern applications while also admitting sta-tistical guarantees.
First, we approach a classical nonparametric regression with a stochastic neural network whose weights are drawn from the Gibbs posterior. To save computational costs when sampling from the Gibbs posterior, a naive stochastic Metropolis-Hastings approach can be used but leads to less ac-curate estimates. However, we demonstrate that this drawback can be avoided with a simple cor-rection term. We prove PAC-Bayes oracle inequalities for the invariant distribution of the resulting algorithm. Further, we investigate size and coverage of credible sets constructed from this invariant distribution. We validate the theoretical merits of our method with a simulation study.
Second, we estimate the jump density of a multivariate Lévy process based on time-discrete ob-servations using the spectral approach. We present uniform risk bounds for our estimator over fully nonparametric classes of Lévy processes under mild assumptions and illustrate the results with a simulation example.
Parts of this talk are based on joint work with Sebastian Bieringer, Gregor Kasieczka and Mathias Trabs.
Dienstag, 09.01.2024, 15.45 Uhr, Ort: SR 1.059
Lea Kunkel (Institut für Stochastik, KIT)
A Wasserstein perspective of Vanilla GANs
Abstract:The empirical success of Generative Adversarial Networks (GANs) caused an increasing interest in theoretical research. The statistical literature is mainly focused on Wasserstein GANs and generalizations thereof, which especially allow for good dimension reduction properties. Statistical results for Vanilla GANs, the original optimization problem, are still rather limited and require assumptions such as smooth activation functions and equal dimensions of the latent space and the ambient space. To bridge this gap, we draw a connection from Vanilla GANs to the Wasserstein distance. By doing so, existing results for Wasserstein GANs can be extended to Vanilla GANs. In particular, we obtain an oracle inequality for Vanilla GANs in Wasserstein distance. The assumptions of this oracle inequality are designed to be satisfied by network architectures commonly used in practice, such as feedforward ReLU networks. Using Hölder-continuous ReLU networks we conclude a rate of convergence for estimating an unknown probability distribution.
Dienstag, 12.12.2023, 15.45 Uhr, Ort: SR 1.059
Prof. Dr. Marko Obradović (University of Belgrad)
Some Equidistribution-type Characterizations of the Exponential Distribution Based on Order Statistics
Abstract: The exponential distribution has got the largest number of characterization theorems, thanks to both its applicability and its simplicity. Several characterization theorems will be shown, which are all based on equality in distribution of some random variables involving order statistics from an iid sample. Their method of proof is based on Maclaurin series expansions and some identities involving Stirling numbers of the second kind. Some applications of these characterizations in goodness-of-fit testing will also be mentioned.
Dienstag, 28.11.2023, 15.45 Uhr, Ort: SR 1.059
Prof. Dr. Siegfried Hörmann (TU Graz)
Measuring dependence between a scalar response and a functional covariate
Abstract: We extend the scope of a recently introduced dependence coefficient between scalar re-sponses and multivariate covariates to the case of functional covariates. While formally the extension is straight forward, the limiting behaviour of the sample version of the coefficient is delicate. It crucially depends on the nearest- neighbour structure of the covariate sam-ple. Essentially, one needs an upper bound for the maximal number of points which share the same nearest neighbour. While a deterministic bound exists for multivariate data, this is no longer the case in infinite dimensional spaces. To our surprise, very little seems to be known about properties of the nearest neighbour graph in a high-dimensional or even functional random sample, and hence we try to advise a way how to overcome this prob-lem. An important application of our theoretical results is a test for independence between scalar responses and functional covariates.
The talk is based on joint work Daniel Strenger.