Nonparametric Bayesian Clustering via Infinite Warped Mixture Models

We introduce a flexible class of mixture models for clustering and density estimation. Our model allows clustering of non-linearly-separable data, produces a potentially low-dimensional latent representation, automatically infers the number of clusters, and produces a density estimate. Our approach makes use of two tools from Bayesian nonparametrics: a Dirichlet process mixture model to allow an unbounded number of clusters, and a Gaussian process warping function to allow each cluster to have a complex shape. 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, and performs much better than infinite Gaussian mixture models at discovering meaningful clusters.