Lower Bounds for the Gibbs Sampler over Mixtures of Gaussians

Christopher Tosh, Sanjoy Dasgupta
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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-tosh14, title = {Lower Bounds for the Gibbs Sampler over Mixtures of Gaussians}, author = {Tosh, Christopher and Dasgupta, Sanjoy}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {1467--1475}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/tosh14.pdf}, url = {https://proceedings.mlr.press/v32/tosh14.html}, 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.} }
Endnote
%0 Conference Paper %T Lower Bounds for the Gibbs Sampler over Mixtures of Gaussians %A Christopher Tosh %A Sanjoy Dasgupta %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-tosh14 %I PMLR %P 1467--1475 %U https://proceedings.mlr.press/v32/tosh14.html %V 32 %N 2 %X 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.
RIS
TY - CPAPER TI - Lower Bounds for the Gibbs Sampler over Mixtures of Gaussians AU - Christopher Tosh AU - Sanjoy Dasgupta BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-tosh14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 1467 EP - 1475 L1 - http://proceedings.mlr.press/v32/tosh14.pdf UR - https://proceedings.mlr.press/v32/tosh14.html AB - 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. ER -
APA
Tosh, C. & Dasgupta, S.. (2014). Lower Bounds for the Gibbs Sampler over Mixtures of Gaussians. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):1467-1475 Available from https://proceedings.mlr.press/v32/tosh14.html.

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