Partition functions from rao-blackwellized tempered sampling

David E. Carlson, Patrick Stinson, Ari Pakman, Liam Paninski

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 multi-modal 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 Boltz-mann Machines (RBM); moreover, the method is sufficiently accurate to track training and validation log-likelihoods during learning of RBMs, at minimal computational cost.

Original languageAmerican English
Title of host publication33rd International Conference on Machine Learning, ICML 2016
EditorsKilian Q. Weinberger, Maria Florina Balcan
Number of pages15
ISBN (Electronic)9781510829008
StatePublished - 1 Jan 2016
Externally publishedYes
Event33rd International Conference on Machine Learning, ICML 2016 - New York City, United States
Duration: 19 Jun 201624 Jun 2016

Publication series

Name33rd International Conference on Machine Learning, ICML 2016


Conference33rd International Conference on Machine Learning, ICML 2016
Country/TerritoryUnited States
CityNew York City

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Computer Networks and Communications


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