The transcoding sampler for stick-breaking inferences on Dirichlet process mixtures
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An issue of Dirichlet process mixture models is the slow mixing of the MCMC posterior chain produced by conditional Gibbs samplers based on its stick-breaking representation, as opposed to marginal collapsed Gibbs samplers based on the Polya urn, which have smaller integrated autocorrelation times. We solve the issue by introducing the transcoding sampler, a new stick-breaking sampler which, conditional to the exchangeable partition posterior produced by any other sampler, enriches it with posterior samples of the stick-breaking parameters. This new sampler is therefore able to match the autocorrelation times of any other sampler, including marginal collapsed Gibbs samplers; it outperforms the slice sampler and removes the need to accelerate it with label-switching Metropolis jumps. As a building block for the transcoding sampler we develop the i.i.d. transcoding algorithm which, conditional to a posterior partition of the data, can infer back which specific stick in the stick-breaking construction each observation originated from.
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