Bayesian Uncertainty Quantification Meets Topology

Sebastian M Schmon, Julius von Rohrscheidt, Bastian Rieck

Keywords: bayesian uncertainty quantification, topological data analysis, persistent homology, topological machine learning, topology, bayesian methods

TL;DR: We develop new Bayesian uncertainty quantification methods based on geometrical and topological losses.

Abstract: Computational topology recently started to emerge as an overarching paradigm for characterising the ‘shape’ of high-dimensional data, leading to powerful algorithms in (un)supervised representation learning. While capable of capturing prominent features at multiple scales, topological methods cannot readily quantify the uncertainty of their respective descriptors. We develop a novel approach that bridges this gap, making it possible to employ topology-based loss functions to perform parameter estimation with Bayesian uncertainty quantification. Our method affords easy integration into topological machine learning algorithms. We demonstrate its efficacy for parameter estimation in different simulation settings.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 5308