Konferenzen

Conferences - Workshops - Seminar Talks

Hyperbolic Geometry for Network Embeddings and Supervised Learning

01. July 2021, 15:00 - 16:00 Uhr
This is a mini-series of two talks related to applications of hyperbolic geometry to embeddings of large graphs and to supervised learning with prototypes
Organizer: Martin Keller-Ressel, TU Dresden
Online-Link

  •  15:00 Uhr  •  "Hydra: A Method for Strain-Minimizing Hyperbolic Embedding of Network- and Distance-Based Data" Stephanie Nargang (TU Dresden)
  •  15:30 Uhr  •   "Hyperbolic Busemann Learning with Ideal Prototypes" Pascal Mettes (University of Amsterdam)

Abstract I: We introduce hydra (hyperbolic distance recovery and approximation), a new method for embedding network- or distance-based data into hyperbolic space. We show mathematically that hydra satisfies a certain optimality guarantee: It minimizes the 'hyperbolic strain' between original and embedded data points. Moreover, it recovers points exactly, when they are located on a hyperbolic submanifold of the feature space. Testing on real network data we show that the embedding quality of hydra is competitive with existing hyperbolic embedding methods, but achieved at substantially shorter computation time. An extended method, termed hydra+, outperforms existing methods in both computation time and embedding quality.

Abstract II : Hyperbolic space has become a popular choice of manifold for representation learning of arbitrary data, from tree-like structures and text to graphs. Building on the success of deep learning with prototypes in Euclidean and hyperspherical spaces, a few recent works have proposed hyperbolic prototypes for classification. Such approaches enable effective learning in low-dimensional output spaces and can exploit hierarchical relations amongst classes, but require privileged information about class labels to position the hyperbolic prototypes. In this work, we propose Hyperbolic Busemann Learning. The main idea behind our approach is to position prototypes on the ideal boundary of the Poincaré ball, which does not require prior label knowledge. To be able to compute proximities to ideal prototypes, we introduce the penalised Busemann loss. We provide theory supporting the use of ideal prototypes and the proposed loss by proving its equivalence to logistic regression in the one-dimensional case. Empirically, we show that our approach provides a natural interpretation of classification confidence, while outperforming recent hyperspherical and hyperbolic prototype approaches.

Talk: "Fluctuations of beta-ensembles in the high temperature regime"

15. July 2021 - Gaultier Lambert
Abstract: I will report on recent results from arXiv:1909.01142 (joint work with Adrien Hardy) and arXiv:1912.10261 on beta-ensembles (and Coulomb gas in higher dimension) in the so-called high temperature regime. I will first explain what is the high temperature regime, how it differs from the usual fixed \beta regime and why it is interesting. Then, I will present different theorems which characterize the fluctuations of the particles in the large N limit. I will first explain the large deviations principle and a central limit theorem which describes the fluctuations of the empirical measure. Then, I will show that local configurations converge to a Poisson point process in the bulk.

Archive

Martin Simon and Eberhard Mayerhofer visiting

Vortrag "Formen der Yield- und Forwardkurve im Langzeitverhalten"

Talk "Semi-Static and Sparse Variance-Optimal Hedging"

Talk: "Relaxed Network Deconvolution"

Talk: "Shapes of Yield- and Forward-Curves in Affine Term Structure Models"

Summer School in Financial Mathematics

Dresden-Wien Workshop

22. April 2017
The Dresden-Wien Workshop on Stochastic Analysis took place from April 20 to April 22 at TU Dresden. It was organised by Prof. Dr. Martin Keller-Ressel und Prof. Dr. Dietmar Ferger, Prof. Dr. Uwe Schmock und Prof. Dr. Mathias Beiglböck.