Partition Functions from Rao-Blackwellized Tempered Sampling

David Carlson, Patrick Stinson, Ari Pakman, Liam Paninski
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:2896-2905, 2016.

Abstract

Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliary inverse temperature variable. Our method exploits the multinomial probability law of the inverse temperatures, and provides estimates of the partition function in terms of a simple quotient of Rao-Blackwellized marginal inverse temperature probability estimates, which are updated while sampling. We show that the method has interesting connections with several alternative popular methods, and offers some significant advantages. In particular, we empirically find that the new method provides more accurate estimates than Annealed Importance Sampling when calculating partition functions of large Restricted Boltzmann Machines (RBM); moreover, the method is sufficiently accurate to track training and validation log-likelihoods during learning of RBMs, at minimal computational cost.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-carlson16, title = {Partition Functions from Rao-Blackwellized Tempered Sampling}, author = {Carlson, David and Stinson, Patrick and Pakman, Ari and Paninski, Liam}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {2896--2905}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/carlson16.pdf}, url = {https://proceedings.mlr.press/v48/carlson16.html}, abstract = {Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliary inverse temperature variable. Our method exploits the multinomial probability law of the inverse temperatures, and provides estimates of the partition function in terms of a simple quotient of Rao-Blackwellized marginal inverse temperature probability estimates, which are updated while sampling. We show that the method has interesting connections with several alternative popular methods, and offers some significant advantages. In particular, we empirically find that the new method provides more accurate estimates than Annealed Importance Sampling when calculating partition functions of large Restricted Boltzmann Machines (RBM); moreover, the method is sufficiently accurate to track training and validation log-likelihoods during learning of RBMs, at minimal computational cost.} }
Endnote
%0 Conference Paper %T Partition Functions from Rao-Blackwellized Tempered Sampling %A David Carlson %A Patrick Stinson %A Ari Pakman %A Liam Paninski %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-carlson16 %I PMLR %P 2896--2905 %U https://proceedings.mlr.press/v48/carlson16.html %V 48 %X Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliary inverse temperature variable. Our method exploits the multinomial probability law of the inverse temperatures, and provides estimates of the partition function in terms of a simple quotient of Rao-Blackwellized marginal inverse temperature probability estimates, which are updated while sampling. We show that the method has interesting connections with several alternative popular methods, and offers some significant advantages. In particular, we empirically find that the new method provides more accurate estimates than Annealed Importance Sampling when calculating partition functions of large Restricted Boltzmann Machines (RBM); moreover, the method is sufficiently accurate to track training and validation log-likelihoods during learning of RBMs, at minimal computational cost.
RIS
TY - CPAPER TI - Partition Functions from Rao-Blackwellized Tempered Sampling AU - David Carlson AU - Patrick Stinson AU - Ari Pakman AU - Liam Paninski BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-carlson16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 2896 EP - 2905 L1 - http://proceedings.mlr.press/v48/carlson16.pdf UR - https://proceedings.mlr.press/v48/carlson16.html AB - Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliary inverse temperature variable. Our method exploits the multinomial probability law of the inverse temperatures, and provides estimates of the partition function in terms of a simple quotient of Rao-Blackwellized marginal inverse temperature probability estimates, which are updated while sampling. We show that the method has interesting connections with several alternative popular methods, and offers some significant advantages. In particular, we empirically find that the new method provides more accurate estimates than Annealed Importance Sampling when calculating partition functions of large Restricted Boltzmann Machines (RBM); moreover, the method is sufficiently accurate to track training and validation log-likelihoods during learning of RBMs, at minimal computational cost. ER -
APA
Carlson, D., Stinson, P., Pakman, A. & Paninski, L.. (2016). Partition Functions from Rao-Blackwellized Tempered Sampling. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:2896-2905 Available from https://proceedings.mlr.press/v48/carlson16.html.

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