Bayesian Computation Meets Topology

Abstract

Computational topology recently started to emerge as a novel 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 be used for Bayesian inference. We develop a novel approach that bridges this gap, making it possible to perform parameter estimation in a Bayesian framework, using topology-based loss functions. Our method affords easy integration into topological machine learning algorithms. We demonstrate its efficacy for parameter estimation in different simulation settings.