Evidence Estimation for Bayesian Partially Observed MRFs

Yutian Chen, Max Welling
Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, PMLR 31:178-186, 2013.

Abstract

Bayesian estimation in Markov random fields is very hard due to the intractability of the partition function. The introduction of hidden units makes the situation even worse due to the presence of potentially very many modes in the posterior distribution. For the first time we propose a comprehensive procedure to address one of the Bayesian estimation problems, approximating the evidence of partially observed MRFs based on the Laplace approximation. We also introduce a number of approximate MCMC-based methods for comparison but find that the Laplace approximation significantly outperforms these.

Cite this Paper

BibTeX
@InProceedings{pmlr-v31-chen13c, title = {Evidence Estimation for Bayesian Partially Observed MRFs}, author = {Chen, Yutian and Welling, Max}, booktitle = {Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics}, pages = {178--186}, year = {2013}, editor = {Carvalho, Carlos M. and Ravikumar, Pradeep}, volume = {31}, series = {Proceedings of Machine Learning Research}, address = {Scottsdale, Arizona, USA}, month = {29 Apr--01 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v31/chen13c.pdf}, url = {https://proceedings.mlr.press/v31/chen13c.html}, abstract = {Bayesian estimation in Markov random fields is very hard due to the intractability of the partition function. The introduction of hidden units makes the situation even worse due to the presence of potentially very many modes in the posterior distribution. For the first time we propose a comprehensive procedure to address one of the Bayesian estimation problems, approximating the evidence of partially observed MRFs based on the Laplace approximation. We also introduce a number of approximate MCMC-based methods for comparison but find that the Laplace approximation significantly outperforms these.} }
Endnote
%0 Conference Paper %T Evidence Estimation for Bayesian Partially Observed MRFs %A Yutian Chen %A Max Welling %B Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2013 %E Carlos M. Carvalho %E Pradeep Ravikumar %F pmlr-v31-chen13c %I PMLR %P 178--186 %U https://proceedings.mlr.press/v31/chen13c.html %V 31 %X Bayesian estimation in Markov random fields is very hard due to the intractability of the partition function. The introduction of hidden units makes the situation even worse due to the presence of potentially very many modes in the posterior distribution. For the first time we propose a comprehensive procedure to address one of the Bayesian estimation problems, approximating the evidence of partially observed MRFs based on the Laplace approximation. We also introduce a number of approximate MCMC-based methods for comparison but find that the Laplace approximation significantly outperforms these.
RIS
TY - CPAPER TI - Evidence Estimation for Bayesian Partially Observed MRFs AU - Yutian Chen AU - Max Welling BT - Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics DA - 2013/04/29 ED - Carlos M. Carvalho ED - Pradeep Ravikumar ID - pmlr-v31-chen13c PB - PMLR DP - Proceedings of Machine Learning Research VL - 31 SP - 178 EP - 186 L1 - http://proceedings.mlr.press/v31/chen13c.pdf UR - https://proceedings.mlr.press/v31/chen13c.html AB - Bayesian estimation in Markov random fields is very hard due to the intractability of the partition function. The introduction of hidden units makes the situation even worse due to the presence of potentially very many modes in the posterior distribution. For the first time we propose a comprehensive procedure to address one of the Bayesian estimation problems, approximating the evidence of partially observed MRFs based on the Laplace approximation. We also introduce a number of approximate MCMC-based methods for comparison but find that the Laplace approximation significantly outperforms these. ER -
APA
Chen, Y. & Welling, M.. (2013). Evidence Estimation for Bayesian Partially Observed MRFs. Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 31:178-186 Available from https://proceedings.mlr.press/v31/chen13c.html.

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