ICML 2018oral7 citations

Topological mixture estimation

Steve Huntsman

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.}
}
Topological mixture estimation · ICML 2018