Warped Mixtures for Nonparametric Cluster Shapes

By Tomoharu Iwata, David Kristjanson Duvenaud, Zoubin Ghahramani. 2012

37 citations recorded by the source corpus.

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.

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Citations in the corpus

Composing graphical models with neural networks for structured representations and fast inference (2016, positive): “By composing a latent GMM with nonlinear observations, we can combine the modeling strengths of both [13], learning both discrete clusters along with non-Gaussian cluster shapes: π ∼ Dir(α), (μk,Σk) iid ∼ NIW(λ), γ ∼ p(γ) zn |π iid ∼ π xn iid ∼ N (μn,Σn), yn |xn, γ iid ∼ N (μ(xn; γ), Σ(xn; γ)).”
Identifying Finite Mixtures of Nonparametric Product Distributions and Causal Inference of Confounders (2013, methodology): “Probabilistic mixture models or other clustering meth-ods can be used to identify the mixture components (clusters) (e.g., Von Luxburg (2007); B¨ohning & Seidel (2003); Rasmussen (2000); Iwata et al. (2013)).”
Structured VAEs: Composing Probabilistic Graphical Models and Variational Autoencoders (2016, methodology): “For example, by using a GMM inside an SVAE, one can express a warped mixture model (Iwata et al., 2013).”