Contrastive Divergence Learning with Chained Belief Propagation

Ding Fan, Xue Yexiang
Proceedings of the 10th International Conference on Probabilistic Graphical Models, PMLR 138:161-172, 2020.

Abstract

Contrastive Divergence (CD) is an important maximum-likelihood learning approach for probabilistic graphical models. CD maximizes the difference in likelihood between the observed data and those sampled from the current model distribution using Markov Chain Monte Carlo (MCMC). Nevertheless, the overall performance of CD is hampered by the slow mixing rate of MCMC in the presence of combinatorial constraints. A competing approach BP-CD replaces MCMC with Belief Propagation (BP). However, their samples are generated from a mean-field approximation, which may be far away from the true distribution. Here we propose contrastive divergence learning with chained belief propagation (BPChain-CD). To generate one sample in CD, we fix one variable at a time based on the marginal distribution computed by BP conditioned on previous variables. We analyze BPChain-CD both theoretically and experimentally. We show that BPChain-CD learns better models compared with BP-CD and CD on a range of maximum-likelihood learning experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v138-fan20a, title = { Contrastive Divergence Learning with Chained Belief Propagation}, author = {Fan, Ding and Yexiang, Xue}, booktitle = {Proceedings of the 10th International Conference on Probabilistic Graphical Models}, pages = {161--172}, year = {2020}, editor = {Jaeger, Manfred and Nielsen, Thomas Dyhre}, volume = {138}, series = {Proceedings of Machine Learning Research}, month = {23--25 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v138/fan20a/fan20a.pdf}, url = {https://proceedings.mlr.press/v138/fan20a.html}, abstract = {Contrastive Divergence (CD) is an important maximum-likelihood learning approach for probabilistic graphical models. CD maximizes the difference in likelihood between the observed data and those sampled from the current model distribution using Markov Chain Monte Carlo (MCMC). Nevertheless, the overall performance of CD is hampered by the slow mixing rate of MCMC in the presence of combinatorial constraints. A competing approach BP-CD replaces MCMC with Belief Propagation (BP). However, their samples are generated from a mean-field approximation, which may be far away from the true distribution. Here we propose contrastive divergence learning with chained belief propagation (BPChain-CD). To generate one sample in CD, we fix one variable at a time based on the marginal distribution computed by BP conditioned on previous variables. We analyze BPChain-CD both theoretically and experimentally. We show that BPChain-CD learns better models compared with BP-CD and CD on a range of maximum-likelihood learning experiments.} }
Endnote
%0 Conference Paper %T Contrastive Divergence Learning with Chained Belief Propagation %A Ding Fan %A Xue Yexiang %B Proceedings of the 10th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2020 %E Manfred Jaeger %E Thomas Dyhre Nielsen %F pmlr-v138-fan20a %I PMLR %P 161--172 %U https://proceedings.mlr.press/v138/fan20a.html %V 138 %X Contrastive Divergence (CD) is an important maximum-likelihood learning approach for probabilistic graphical models. CD maximizes the difference in likelihood between the observed data and those sampled from the current model distribution using Markov Chain Monte Carlo (MCMC). Nevertheless, the overall performance of CD is hampered by the slow mixing rate of MCMC in the presence of combinatorial constraints. A competing approach BP-CD replaces MCMC with Belief Propagation (BP). However, their samples are generated from a mean-field approximation, which may be far away from the true distribution. Here we propose contrastive divergence learning with chained belief propagation (BPChain-CD). To generate one sample in CD, we fix one variable at a time based on the marginal distribution computed by BP conditioned on previous variables. We analyze BPChain-CD both theoretically and experimentally. We show that BPChain-CD learns better models compared with BP-CD and CD on a range of maximum-likelihood learning experiments.
APA
Fan, D. & Yexiang, X.. (2020). Contrastive Divergence Learning with Chained Belief Propagation. Proceedings of the 10th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 138:161-172 Available from https://proceedings.mlr.press/v138/fan20a.html.

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