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Topological Mixture Estimation

2020-03-16 | |  63 |   44 |   0

Abstract

We introduce topological mixture estimation, a completely nonparametric and computationally efficient solution to the problem of estimating a one-dimensional mixture with generic unimodal components. We repeatedly perturb the unimodal decomposition of Baryshnikov and Ghrist to produce a topologically and information-theoretically optimal unimodal mixture. We also detail a smoothing process that optimally exploits topological persistence of the unimodal category in a natural way when working directly with sample data. Finally, we illustrate these techniques through examples.

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