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# Lower Bounds for the Gibbs Sampler over Mixtures of Gaussians

*Proceedings of the 31st International Conference on Machine Learning*, PMLR 32(2):1467-1475, 2014.

#### Abstract

The mixing time of a Markov chain is the minimum time t necessary for the total variation distance between the distribution of the Markov chain’s current state X_t and its stationary distribution to fall below some ε> 0. In this paper, we present lower bounds for the mixing time of the Gibbs sampler over Gaussian mixture models with Dirichlet priors.