Warped Mixtures for Nonparametric Cluster Shapes

Tomoharu Iwata, David Duvenaud, Zoubin Ghahramani
Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, PMLR R11:461-470, 2013.

Abstract

A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allows us to summarize the properties of the high-dimensional clusters (or density manifolds) describing the data. The number of manifolds, as well as the shape and dimension of each manifold is automat- ically inferred. We derive a simple inference scheme for this model which analytically inte- grates out both the mixture parameters and the warping function. We show that our model is effective for density estimation, per- forms better than infinite Gaussian mixture models at recovering the true number of clus- ters, and produces interpretable summaries of high-dimensional datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR11-iwata13a, title = {Warped Mixtures for Nonparametric Cluster Shapes}, author = {Iwata, Tomoharu and Duvenaud, David and Ghahramani, Zoubin}, booktitle = {Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence}, pages = {461--470}, year = {2013}, editor = {Nicholson, Ann and Smyth, Padhraic}, volume = {R11}, series = {Proceedings of Machine Learning Research}, month = {12--14 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r11/main/assets/iwata13a/iwata13a.pdf}, url = {https://proceedings.mlr.press/r11/iwata13a.html}, abstract = {A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allows us to summarize the properties of the high-dimensional clusters (or density manifolds) describing the data. The number of manifolds, as well as the shape and dimension of each manifold is automat- ically inferred. We derive a simple inference scheme for this model which analytically inte- grates out both the mixture parameters and the warping function. We show that our model is effective for density estimation, per- forms better than infinite Gaussian mixture models at recovering the true number of clus- ters, and produces interpretable summaries of high-dimensional datasets.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Warped Mixtures for Nonparametric Cluster Shapes %A Tomoharu Iwata %A David Duvenaud %A Zoubin Ghahramani %B Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2013 %E Ann Nicholson %E Padhraic Smyth %F pmlr-vR11-iwata13a %I PMLR %P 461--470 %U https://proceedings.mlr.press/r11/iwata13a.html %V R11 %X A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allows us to summarize the properties of the high-dimensional clusters (or density manifolds) describing the data. The number of manifolds, as well as the shape and dimension of each manifold is automat- ically inferred. We derive a simple inference scheme for this model which analytically inte- grates out both the mixture parameters and the warping function. We show that our model is effective for density estimation, per- forms better than infinite Gaussian mixture models at recovering the true number of clus- ters, and produces interpretable summaries of high-dimensional datasets. %Z Reissued by PMLR on 04 October 2026.
APA
Iwata, T., Duvenaud, D. & Ghahramani, Z.. (2013). Warped Mixtures for Nonparametric Cluster Shapes. Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R11:461-470 Available from https://proceedings.mlr.press/r11/iwata13a.html. Reissued by PMLR on 04 October 2026.

Related Material