ICML 2018oral7 citations
Topological mixture estimation
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.
BibTeX
@InProceedings{pmlr-v80-huntsman18a,
title = {Topological mixture estimation},
author = {Huntsman, Steve},
booktitle = {Proceedings of the 35th International Conference on Machine Learning},
pages = {2088--2097},
year = {2018},
editor = {Dy, Jennifer and Krause, Andreas},
volume = {80},
series = {Proceedings of Machine Learning Research},
month = {10--15 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v80/huntsman18a/huntsman18a.pdf},
url = {https://proceedings.mlr.press/v80/huntsman18a.html},
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.}
}