Welcome to the website of the AIDOS LAB at the Institute of AI for
Health, an institute of
Helmholtz Munich! We are fascinated by
discovering hidden structures in complex data sets, in particular those
arising in healthcare applications.
Our primary research interests are situated at the intersection of
geometry, topology, and machine learning.
We want to make use of geometrical and
topological information to imbue
neural networks with more information in their respective tasks, leading
to better and more robust outcomes.
Along the way, we develop new manifold learning techniques, new
representation learning algorithms, and much more.
Following the dictum ’theory without practice is empty,’ we
address challenges in biomedicine and healthcare
applications.
Curvature Filtrations for Graph Generative Model Evaluation NeurIPS 2023
In response to rising interest for generative model use in drug development,
we introduce a new topological and geometric descriptor
for graph distributions based on curvature filtrations. As well as favorable
stability and expressivity properties, our method affords
scalable statistical comparisons and hypothesis testing for sets of graphs, providing
an exciting and well-principled method for evaluating Graph Generative Models.
Topological Singularity Detection at Multiple Scales ICML 2023
The manifold hypothesis is often assumed in data analysis. But what
happens if it does not hold? In this publication, we are analysing to
what extent a data set deviates from being a manifold. We develop
Euclidicity, a new multi-scale score based on persistent local
homology, to assess this deviation.
Ollivier–Ricci Curvature for Hypergraphs: A Unified Framework ICLR 2023
Bridging geometry and topology, curvature is a powerful and expressive
invariant. While the utility of curvature has been theoretically and
empirically confirmed in the context of manifolds and graphs, its
generalisation to the emerging domain of hypergraphs has remained
largely unexplored. Our paper aims to fill this gap and presents a new
framework for hypergraph curvature.
