Search Results for author: Bastian Rieck

Found 50 papers, 28 papers with code

The Manifold Density Function: An Intrinsic Method for the Validation of Manifold Learning

no code implementations14 Feb 2024 Benjamin Holmgren, Eli Quist, Jordan Schupbach, Brittany Terese Fasy, Bastian Rieck

We introduce the manifold density function, which is an intrinsic method to validate manifold learning techniques.

Mapping the Multiverse of Latent Representations

no code implementations2 Feb 2024 Jeremy Wayland, Corinna Coupette, Bastian Rieck

Echoing recent calls to counter reliability and robustness concerns in machine learning via multiverse analysis, we present PRESTO, a principled framework for mapping the multiverse of machine-learning models that rely on latent representations.


Simplicial Representation Learning with Neural $k$-Forms

1 code implementation13 Dec 2023 Kelly Maggs, Celia Hacker, Bastian Rieck

In this paper, we take a different approach, focusing on leveraging geometric information from simplicial complexes embedded in $\mathbb{R}^n$ using node coordinates.

Representation Learning

Metric Space Magnitude for Evaluating the Diversity of Latent Representations

no code implementations27 Nov 2023 Katharina Limbeck, Rayna Andreeva, Rik Sarkar, Bastian Rieck

We develop a family of magnitude-based measures of the intrinsic diversity of latent representations, formalising a novel notion of dissimilarity between magnitude functions of finite metric spaces.

Dimensionality Reduction Representation Learning

Differentiable Euler Characteristic Transforms for Shape Classification

1 code implementation11 Oct 2023 Ernst Roell, Bastian Rieck

The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs.

Classification Point Cloud Classification

Filtration Surfaces for Dynamic Graph Classification

1 code implementation7 Sep 2023 Franz Srambical, Bastian Rieck

Existing approaches for classifying dynamic graphs either lift graph kernels to the temporal domain, or use graph neural networks (GNNs).

Graph Classification

Topologically Regularized Multiple Instance Learning to Harness Data Scarcity

no code implementations26 Jul 2023 Salome Kazeminia, Carsten Marr, Bastian Rieck

In biomedical data analysis, Multiple Instance Learning (MIL) models have emerged as a powerful tool to classify patients' microscopy samples.

Inductive Bias Multiple Instance Learning

Evaluating the "Learning on Graphs" Conference Experience

no code implementations1 Jun 2023 Bastian Rieck, Corinna Coupette

With machine learning conferences growing ever larger, and reviewing processes becoming increasingly elaborate, more data-driven insights into their workings are required.

MAGNet: Motif-Agnostic Generation of Molecules from Shapes

1 code implementation30 May 2023 Leon Hetzel, Johanna Sommer, Bastian Rieck, Fabian Theis, Stephan Günnemann

Recent advances in machine learning for molecules exhibit great potential for facilitating drug discovery from in silico predictions.

Drug Discovery

Metric Space Magnitude and Generalisation in Neural Networks

no code implementations9 May 2023 Rayna Andreeva, Katharina Limbeck, Bastian Rieck, Rik Sarkar

Deep learning models have seen significant successes in numerous applications, but their inner workings remain elusive.

Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices

no code implementations8 Mar 2023 Kalyan Varma Nadimpalli, Amit Chattopadhyay, Bastian Rieck

We also show a favourable property, namely injectivity and discuss the stability of the topological loss function based on the Euler Characteristic Transform.

Inductive Bias

On the Expressivity of Persistent Homology in Graph Learning

no code implementations20 Feb 2023 Bastian Rieck

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification.

Graph Classification Graph Learning

Curvature Filtrations for Graph Generative Model Evaluation

1 code implementation NeurIPS 2023 Joshua Southern, Jeremy Wayland, Michael Bronstein, Bastian Rieck

Graph generative model evaluation necessitates understanding differences between graphs on the distributional level.

Topological Data Analysis

Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework

1 code implementation21 Oct 2022 Corinna Coupette, Sebastian Dalleiger, Bastian Rieck

Bridging geometry and topology, curvature is a powerful and expressive invariant.

Topological Singularity Detection at Multiple Scales

1 code implementation30 Sep 2022 Julius von Rohrscheidt, Bastian Rieck

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research.

A Diffusion Model Predicts 3D Shapes from 2D Microscopy Images

1 code implementation30 Aug 2022 Dominik J. E. Waibel, Ernst Röell, Bastian Rieck, Raja Giryes, Carsten Marr

Diffusion models are a special type of generative model, capable of synthesising new data from a learnt distribution.

Data Augmentation

On the Surprising Behaviour of node2vec

1 code implementation16 Jun 2022 Celia Hacker, Bastian Rieck

Graph embedding techniques are a staple of modern graph learning research.

Graph Embedding Graph Learning

All the World's a (Hyper)Graph: A Data Drama

2 code implementations16 Jun 2022 Corinna Coupette, Jilles Vreeken, Bastian Rieck

We introduce Hyperbard, a dataset of diverse relational data representations derived from Shakespeare's plays.

Graph Learning Graph Mining

Time-inhomogeneous diffusion geometry and topology

no code implementations28 Mar 2022 Guillaume Huguet, Alexander Tong, Bastian Rieck, Jessie Huang, Manik Kuchroo, Matthew Hirn, Guy Wolf, Smita Krishnaswamy

From a geometric perspective, we obtain convergence bounds based on the smallest transition probability and the radius of the data, whereas from a spectral perspective, our bounds are based on the eigenspectrum of the diffusion kernel.

Clustering Denoising +1

Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstruction

1 code implementation3 Mar 2022 Dominik J. E. Waibel, Scott Atwell, Matthias Meier, Carsten Marr, Bastian Rieck

We propose to complement geometrical shape information by including multi-scale topological features, such as connected components, cycles, and voids, in the reconstruction loss.

3D Reconstruction

On Measuring Excess Capacity in Neural Networks

1 code implementation16 Feb 2022 Florian Graf, Sebastian Zeng, Bastian Rieck, Marc Niethammer, Roland Kwitt

We study the excess capacity of deep networks in the context of supervised classification.

Weisfeiler and Leman go Machine Learning: The Story so far

no code implementations18 Dec 2021 Christopher Morris, Yaron Lipman, Haggai Maron, Bastian Rieck, Nils M. Kriege, Martin Grohe, Matthias Fey, Karsten Borgwardt

In recent years, algorithms and neural architectures based on the Weisfeiler--Leman algorithm, a well-known heuristic for the graph isomorphism problem, have emerged as a powerful tool for machine learning with graphs and relational data.

BIG-bench Machine Learning Representation Learning

Interpretability Aware Model Training to Improve Robustness against Out-of-Distribution Magnetic Resonance Images in Alzheimer's Disease Classification

no code implementations15 Nov 2021 Merel Kuijs, Catherine R. Jutzeler, Bastian Rieck, Sarah C. Brüningk

Owing to its pristine soft-tissue contrast and high resolution, structural magnetic resonance imaging (MRI) is widely applied in neurology, making it a valuable data source for image-based machine learning (ML) and deep learning applications.

The magnitude vector of images

1 code implementation28 Oct 2021 Michael F. Adamer, Edward De Brouwer, Leslie O'Bray, Bastian Rieck

Furthermore, we demonstrate practical use cases of magnitude for machine learning applications and propose a novel magnitude model that consists of a computationally efficient magnitude computation and a learnable metric.

Boundary Detection Descriptive +2

Topological Graph Neural Networks

1 code implementation ICLR 2022 Max Horn, Edward De Brouwer, Michael Moor, Yves Moreau, Bastian Rieck, Karsten Borgwardt

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles.

Graph Learning Node Classification

Exploring the Geometry and Topology of Neural Network Loss Landscapes

no code implementations31 Jan 2021 Stefan Horoi, Jessie Huang, Bastian Rieck, Guillaume Lajoie, Guy Wolf, Smita Krishnaswamy

This suggests that qualitative and quantitative examination of the loss landscape geometry could yield insights about neural network generalization performance during training.

Dimensionality Reduction

Topological Data Analysis of copy number alterations in cancer

no code implementations22 Nov 2020 Stefan Groha, Caroline Weis, Alexander Gusev, Bastian Rieck

Identifying subgroups and properties of cancer biopsy samples is a crucial step towards obtaining precise diagnoses and being able to perform personalized treatment of cancer patients.

Topological Data Analysis

Image analysis for Alzheimer's disease prediction: Embracing pathological hallmarks for model architecture design

no code implementations12 Nov 2020 Sarah C. Brüningk, Felix Hensel, Catherine R. Jutzeler, Bastian Rieck

Alzheimer's disease (AD) is associated with local (e. g. brain tissue atrophy) and global brain changes (loss of cerebral connectivity), which can be detected by high-resolution structural magnetic resonance imaging.

Disease Prediction

Graph Kernels: State-of-the-Art and Future Challenges

1 code implementation7 Nov 2020 Karsten Borgwardt, Elisabetta Ghisu, Felipe Llinares-López, Leslie O'Bray, Bastian Rieck

Graph-structured data are an integral part of many application domains, including chemoinformatics, computational biology, neuroimaging, and social network analysis.


Challenging Euclidean Topological Autoencoders

1 code implementation NeurIPS Workshop TDA_and_Beyond 2020 Michael Moor, Max Horn, Karsten Borgwardt, Bastian Rieck

Topological autoencoders (TopoAE) have demonstrated their capabilities for performing dimensionality reduction while at the same time preserving topological information of the input space.

Dimensionality Reduction

Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence

1 code implementation NeurIPS 2020 Bastian Rieck, Tristan Yates, Christian Bock, Karsten Borgwardt, Guy Wolf, Nicholas Turk-Browne, Smita Krishnaswamy

We observe significant differences in both brain state trajectories and overall topological activity between adults and children watching the same movie.


Path Imputation Strategies for Signature Models of Irregular Time Series

2 code implementations25 May 2020 Michael Moor, Max Horn, Christian Bock, Karsten Borgwardt, Bastian Rieck

The signature transform is a 'universal nonlinearity' on the space of continuous vector-valued paths, and has received attention for use in machine learning on time series.

Imputation Irregular Time Series +2

Set Functions for Time Series

2 code implementations ICML 2020 Max Horn, Michael Moor, Christian Bock, Bastian Rieck, Karsten Borgwardt

Despite the eminent successes of deep neural networks, many architectures are often hard to transfer to irregularly-sampled and asynchronous time series that commonly occur in real-world datasets, especially in healthcare applications.

Time Series Time Series Analysis +1

Topological Machine Learning with Persistence Indicator Functions

no code implementations31 Jul 2019 Bastian Rieck, Filip Sadlo, Heike Leitte

Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis.

BIG-bench Machine Learning Topological Data Analysis

Persistent Intersection Homology for the Analysis of Discrete Data

no code implementations31 Jul 2019 Bastian Rieck, Markus Banagl, Filip Sadlo, Heike Leitte

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets.

Topological Data Analysis

Wasserstein Weisfeiler-Lehman Graph Kernels

2 code implementations NeurIPS 2019 Matteo Togninalli, Elisabetta Ghisu, Felipe Llinares-López, Bastian Rieck, Karsten Borgwardt

Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures.

Graph Classification

Topological Autoencoders

2 code implementations ICML 2020 Michael Moor, Max Horn, Bastian Rieck, Karsten Borgwardt

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders.

Topological Data Analysis

Graph Filtration Learning

1 code implementation ICML 2020 Christoph D. Hofer, Florian Graf, Bastian Rieck, Marc Niethammer, Roland Kwitt

We propose an approach to learning with graph-structured data in the problem domain of graph classification.

General Classification Graph Classification

Early Recognition of Sepsis with Gaussian Process Temporal Convolutional Networks and Dynamic Time Warping

2 code implementations5 Feb 2019 Michael Moor, Max Horn, Bastian Rieck, Damian Roqueiro, Karsten Borgwardt

This empirical study proposes two novel approaches for the early detection of sepsis: a deep learning model and a lazy learner based on time series distances.

Dynamic Time Warping Management +3

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