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Causality and Physics-informed Machine Learning

Research Project
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01.01.2017
 - 31.12.2025

Describing and discovering causal relationships is a concept at the crossroads of philosophy, mathematics and statistics. It has recently gained popularity in the machine learning community. While statistical dependence tells us when two variables tend to change simultaneously, causal models aim at making statements about a direction behind this simultaneousness. Models of causal relationships thus allow questions like ("Does smoking increase the probability of developing an illness?", "What happens to a phenotype if a gene is knocked out?" or "What happens to a system if one of its variables is set to a given value?") to be tackled. A number of approaches to modelling causality have been proposed, ranging from ones based purely on observational data (i.e. passive observation of a system) through mixed data to interventional (experimental) data, where an experiment controlling for a particular variable has been performed. Possible application areas include, among others, genetic and biomedical data, social network analysis or financial data. We focus on the approach where the relationship between observational and interventional distributions is a measure of causality and is quantified with information theoretic tools. Building on that, we propose methods of time series modelling, causal graph recovery and causal segmentation. We apply the approach to genetic and EEG data.

Publications

Arend Torres, Fabricio et al. (2024) ‘Lagrangian Flow Networks for Conservation Laws’, in The Twelfth International Conference on Learning Representations. Vienna, Austria (The Twelfth International Conference on Learning Representations). Available at: https://openreview.net/forum?id=Nshk5YpdWE.

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Nagy-Huber, Monika and Roth, Volker (2024) ‘Physics-informed boundary integral networks (PIBI-Nets): A data-driven approach for solving partial differential equations’, Journal of Computational Science, 81. Available at: https://doi.org/10.1016/j.jocs.2024.102355.

URLs
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Negri, Marcello Massimo, Arend Torres, Fabricio and Roth, Volker (2023) ‘Conditional Matrix Flows for Gaussian Graphical Models’, in Advances in Neural Information Processing Systems. New Orleans: Curran Associates, Inc. (Advances in Neural Information Processing Systems), pp. 25095––25111. Available at: https://proceedings.neurips.cc/paper_files/paper/2023/file/4eef8829319316d0b552328715c836c3-Paper-Conference.pdf.

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Arend Torres, Fabricio et al. (2022) ‘Mesh-free eulerian physics-informed neural networks’. Available at: https://doi.org/10.48550/arxiv.2206.01545.

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Parbhoo, Sonali et al. (2020) ‘Information Bottleneck for Estimating Treatment Effects with Systematically Missing Covariates’, Entropy, 22(4), p. 389. Available at: https://doi.org/10.3390/e22040389.

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Wieczorek, Aleksander and Roth, Volker (2020) ‘On the Difference between the Information Bottleneck and the Deep Information Bottleneck’, Entropy, 22(2), p. 131. Available at: https://doi.org/10.3390/e22020131.

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Wieser, Mario et al. (2020) ‘Inverse Learning of Symmetries’, in Larochelle, H.; Ranzato, M.; Hadsell, R.; Balcan, M. F.; Lin, H. (ed.). Curran Associates, Inc.: Curran Associates, Inc.

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Wieczorek, Aleksander and Roth, Volker (2019) ‘Information Theoretic Causal Effect Quantification’, Entropy, 21(10), p. 975. Available at: https://doi.org/10.3390/e21100975.

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Wieczorek, Aleksander et al. (2018) ‘Learning sparse latent representations with the deep copula information bottleneck’.

Members (4)

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Volker Roth

Principal Investigator
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Aleksander Wieczorek

Project Member
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Marcello Massimo Negri

Project Member
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Monika Timea Nagy-Huber

Project Member