Modal-set estimation with an application to clustering

Heinrich Jiang, Samory Kpotufe
; Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:1197-1206, 2017.

Abstract

We present a procedure that can estimate – with statistical consistency guarantees – any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or modal-sets, of any bounded shape or dimension, including usual point-modes. In practice, modal-sets can arise as dense low-dimensional structures in noisy data, and more generally serve to better model the rich variety of locally dense structures in data. The procedure is then shown to be competitive on clustering applications, and moreover is quite stable to a wide range of settings of its tuning parameter.

Cite this Paper


BibTeX
@InProceedings{pmlr-v54-jiang17c, title = {{Modal-set estimation with an application to clustering}}, author = {Heinrich Jiang and Samory Kpotufe}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {1197--1206}, year = {2017}, editor = {Aarti Singh and Jerry Zhu}, volume = {54}, series = {Proceedings of Machine Learning Research}, address = {Fort Lauderdale, FL, USA}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/jiang17c/jiang17c.pdf}, url = {http://proceedings.mlr.press/v54/jiang17c.html}, abstract = {We present a procedure that can estimate – with statistical consistency guarantees – any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or modal-sets, of any bounded shape or dimension, including usual point-modes. In practice, modal-sets can arise as dense low-dimensional structures in noisy data, and more generally serve to better model the rich variety of locally dense structures in data. The procedure is then shown to be competitive on clustering applications, and moreover is quite stable to a wide range of settings of its tuning parameter. } }
Endnote
%0 Conference Paper %T Modal-set estimation with an application to clustering %A Heinrich Jiang %A Samory Kpotufe %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-jiang17c %I PMLR %J Proceedings of Machine Learning Research %P 1197--1206 %U http://proceedings.mlr.press %V 54 %W PMLR %X We present a procedure that can estimate – with statistical consistency guarantees – any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or modal-sets, of any bounded shape or dimension, including usual point-modes. In practice, modal-sets can arise as dense low-dimensional structures in noisy data, and more generally serve to better model the rich variety of locally dense structures in data. The procedure is then shown to be competitive on clustering applications, and moreover is quite stable to a wide range of settings of its tuning parameter.
APA
Jiang, H. & Kpotufe, S.. (2017). Modal-set estimation with an application to clustering. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in PMLR 54:1197-1206

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