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 automatically inferred. We derive a simple inference scheme for this model which analytically integrates out both the mixture parameters and the warping function. We show that our model is effective for density estimation, performs better than infinite Gaussian mixture models at recovering the true number of clusters, 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 automatically inferred. We derive a simple inference scheme for this model which analytically integrates out both the mixture parameters and the warping function. We show that our model is effective for density estimation, performs better than infinite Gaussian mixture models at recovering the true number of clusters, 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 automatically inferred. We derive a simple inference scheme for this model which analytically integrates out both the mixture parameters and the warping function. We show that our model is effective for density estimation, performs better than infinite Gaussian mixture models at recovering the true number of clusters, 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.

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