Topological mixture estimation
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:20882097, 2018.
Abstract
We introduce topological mixture estimation, a completely nonparametric and computationally efficient solution to the problem of estimating a onedimensional mixture with generic unimodal components. We repeatedly perturb the unimodal decomposition of Baryshnikov and Ghrist to produce a topologically and informationtheoretically 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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