Topological mixture estimation

Steve Huntsman
; Proceedings of the 35th International Conference on Machine Learning, PMLR 80:2088-2097, 2018.

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.

Cite this Paper


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 = {Jennifer Dy and Andreas Krause}, volume = {80}, series = {Proceedings of Machine Learning Research}, address = {Stockholmsmässan, Stockholm Sweden}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/huntsman18a/huntsman18a.pdf}, url = {http://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.} }
Endnote
%0 Conference Paper %T Topological mixture estimation %A Steve Huntsman %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-huntsman18a %I PMLR %J Proceedings of Machine Learning Research %P 2088--2097 %U http://proceedings.mlr.press %V 80 %W PMLR %X 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.
APA
Huntsman, S.. (2018). Topological mixture estimation. Proceedings of the 35th International Conference on Machine Learning, in PMLR 80:2088-2097

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