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  1. Book ; Online: On the Expressivity of Persistent Homology in Graph Learning

    Rieck, Bastian

    2023  

    Abstract: Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features, such as cycles ... ...

    Abstract Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features, such as cycles of arbitrary length, in combination with multi-scale topological descriptors, has improved predictive performance for data sets with prominent topological structures, such as molecules. At the same time, the theoretical properties of persistent homology have not been formally assessed in this context. This paper intends to bridge the gap between computational topology and graph machine learning by providing a brief introduction to persistent homology in the context of graphs, as well as a theoretical discussion and empirical analysis of its expressivity for graph learning tasks.
    Keywords Computer Science - Machine Learning ; Mathematics - Algebraic Topology ; Statistics - Machine Learning ; 55N31 (Primary) 62R40 ; 68T09 (Secondary)
    Subject code 514
    Publishing date 2023-02-20
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

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  2. Article ; Online: A Note on Cherry-Picking in Meta-Analyses.

    Yoneoka, Daisuke / Rieck, Bastian

    Entropy (Basel, Switzerland)

    2023  Volume 25, Issue 4

    Abstract: We study selection bias in meta-analyses by assuming the presence of researchers (meta-analysts) who intentionally or unintentionally cherry-pick a subset of studies by defining arbitrary inclusion and/or exclusion criteria that will lead to their ... ...

    Abstract We study selection bias in meta-analyses by assuming the presence of researchers (meta-analysts) who intentionally or unintentionally cherry-pick a subset of studies by defining arbitrary inclusion and/or exclusion criteria that will lead to their desired results. When the number of studies is sufficiently large, we theoretically show that a meta-analysts might falsely obtain (non)significant overall treatment effects, regardless of the actual effectiveness of a treatment. We analyze all theoretical findings based on extensive simulation experiments and practical clinical examples. Numerical evaluations demonstrate that the standard method for meta-analyses has the potential to be cherry-picked.
    Language English
    Publishing date 2023-04-19
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e25040691
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  3. Book ; Online: Basic Analysis of Bin-Packing Heuristics

    Rieck, Bastian

    2021  

    Abstract: The bin-packing problem continues to remain relevant in numerous application areas. This technical report discusses the empirical performance of different bin-packing heuristics for certain test problems. ...

    Abstract The bin-packing problem continues to remain relevant in numerous application areas. This technical report discusses the empirical performance of different bin-packing heuristics for certain test problems.
    Keywords Mathematics - Optimization and Control ; Computer Science - Data Structures and Algorithms
    Publishing date 2021-04-25
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Book ; Online: Evaluating the "Learning on Graphs" Conference Experience

    Rieck, Bastian / Coupette, Corinna

    2023  

    Abstract: With machine learning conferences growing ever larger, and reviewing processes becoming increasingly elaborate, more data-driven insights into their workings are required. In this report, we present the results of a survey accompanying the first " ... ...

    Abstract With machine learning conferences growing ever larger, and reviewing processes becoming increasingly elaborate, more data-driven insights into their workings are required. In this report, we present the results of a survey accompanying the first "Learning on Graphs" (LoG) Conference. The survey was directed to evaluate the submission and review process from different perspectives, including authors, reviewers, and area chairs alike.
    Keywords Computer Science - Machine Learning ; Computer Science - Computers and Society
    Publishing date 2023-06-01
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

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  5. Book ; Online: Differentiable Euler Characteristic Transforms for Shape Classification

    Roell, Ernst / Rieck, Bastian

    2023  

    Abstract: The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs. However, the ECT was hitherto unable to learn task-specific representations. We overcome this ...

    Abstract The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs. However, the ECT was hitherto unable to learn task-specific representations. We overcome this issue and develop a novel computational layer that enables learning the ECT in an end-to-end fashion. Our method DECT is fast and computationally efficient, while exhibiting performance on a par with more complex models in both graph and point cloud classification tasks. Moreover, we show that this seemingly unexpressive statistic still provides the same topological expressivity as more complex topological deep learning layers provide.
    Keywords Computer Science - Machine Learning
    Publishing date 2023-10-11
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

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  6. Book ; Online: Topological Singularity Detection at Multiple Scales

    von Rohrscheidt, Julius / Rieck, Bastian

    2022  

    Abstract: 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. However, recent work has shown that real-world data exhibits distinct non-manifold ... ...

    Abstract 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. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the 'manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.

    Comment: Accepted at the International Conference on Machine Learning (ICML) 2023; camera-ready version
    Keywords Computer Science - Machine Learning ; Computer Science - Artificial Intelligence ; Mathematics - Algebraic Topology ; Statistics - Machine Learning ; 55N31 (Primary) ; 32S50 (Secondary)
    Subject code 006
    Publishing date 2022-09-30
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

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  7. Book ; Online: On the Surprising Behaviour of node2vec

    Hacker, Celia / Rieck, Bastian

    2022  

    Abstract: Graph embedding techniques are a staple of modern graph learning research. When using embeddings for downstream tasks such as classification, information about their stability and robustness, i.e., their susceptibility to sources of noise, stochastic ... ...

    Abstract Graph embedding techniques are a staple of modern graph learning research. When using embeddings for downstream tasks such as classification, information about their stability and robustness, i.e., their susceptibility to sources of noise, stochastic effects, or specific parameter choices, becomes increasingly important. As one of the most prominent graph embedding schemes, we focus on node2vec and analyse its embedding quality from multiple perspectives. Our findings indicate that embedding quality is unstable with respect to parameter choices, and we propose strategies to remedy this in practice.

    Comment: ICML 2022 Workshop on Topology, Algebra, and Geometry in Machine Learning (Camera-Ready Version)
    Keywords Computer Science - Machine Learning ; Statistics - Machine Learning
    Publishing date 2022-06-16
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  8. Book ; Online: Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices

    Nadimpalli, Kalyan Varma / Chattopadhyay, Amit / Rieck, Bastian

    2023  

    Abstract: The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which may lead to ... ...

    Abstract The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which may lead to poor reconstructions as they ignore the structural properties of the shape. To tackle this, we propose a novel topological loss function based on the Euler Characteristic Transform. This loss can be used as an inductive bias to aid the optimization of any neural network toward better reconstructions in the regime of limited data. We show the effectiveness of the proposed loss function by incorporating it into SHAPR, a state-of-the-art shape reconstruction model, and test it on two benchmark datasets, viz., Red Blood Cells and Nuclei datasets. We also show a favourable property, namely injectivity and discuss the stability of the topological loss function based on the Euler Characteristic Transform.

    Comment: e-print
    Keywords Computer Science - Machine Learning ; Quantitative Biology - Quantitative Methods
    Subject code 006
    Publishing date 2023-03-07
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

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  9. Book ; Online: DONUT -- Creation, Development, and Opportunities of a Database

    Giunti, Barbara / Lazovskis, Jānis / Rieck, Bastian

    2023  

    Abstract: DONUT is a database of papers about practical, real-world uses of Topological Data Analysis (TDA). Its original seed was planted in a group chat formed during the HIM Spring School on Applied and Computational Algebraic Topology in April 2017. This ... ...

    Abstract DONUT is a database of papers about practical, real-world uses of Topological Data Analysis (TDA). Its original seed was planted in a group chat formed during the HIM Spring School on Applied and Computational Algebraic Topology in April 2017. This document describes the creation, curation, and maintenance process of the database.
    Keywords Computer Science - Digital Libraries ; Computer Science - Databases ; Mathematics - Algebraic Topology
    Publishing date 2023-04-24
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

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  10. Book ; Online: Metric Space Magnitude and Generalisation in Neural Networks

    Andreeva, Rayna / Limbeck, Katharina / Rieck, Bastian / Sarkar, Rik

    2023  

    Abstract: Deep learning models have seen significant successes in numerous applications, but their inner workings remain elusive. The purpose of this work is to quantify the learning process of deep neural networks through the lens of a novel topological invariant ...

    Abstract Deep learning models have seen significant successes in numerous applications, but their inner workings remain elusive. The purpose of this work is to quantify the learning process of deep neural networks through the lens of a novel topological invariant called magnitude. Magnitude is an isometry invariant; its properties are an active area of research as it encodes many known invariants of a metric space. We use magnitude to study the internal representations of neural networks and propose a new method for determining their generalisation capabilities. Moreover, we theoretically connect magnitude dimension and the generalisation error, and demonstrate experimentally that the proposed framework can be a good indicator of the latter.
    Keywords Computer Science - Machine Learning ; Mathematics - Geometric Topology ; Statistics - Machine Learning
    Publishing date 2023-05-09
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

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