Estimating the Partition Function by Discriminance Sampling

Qiang Liu, Jian Peng UIUC, Alexander Ihler, John Fisher III
Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, PMLR R13:358-366, 2015.

Abstract

Importance sampling (IS) and its variant, annealed IS (AIS) have been widely used for estimating the partition function in graphical models, such as Markov random fields and deep generative models. However, IS tends to underestimate the partition function and is subject to high variance when the proposal distribution is more peaked than the target distribution. On the other hand, "reverse" versions of IS and AIS tend to overestimate the partition function, and degenerate when the target distribution is more peaked than the proposal distribution. In this work, we present a simple, general method that gives much more reliable and robust estimates than either IS (AIS) or reverse IS (AIS). Our method works by converting the estimation problem into a simple classification problem that discriminates between the samples drawn from the target and the proposal. We give extensive theoretical and empirical justification; in particular, we show that an annealed version of our method significantly outperforms both AIS and reverse AIS as proposed by Burda et al. (2015), which has been the state-of-the-art for likelihood evaluation in deep learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR13-liu15c, title = {Estimating the Partition Function by Discriminance Sampling}, author = {Liu, Qiang and UIUC, Jian Peng and Ihler, Alexander and III, John Fisher}, booktitle = {Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence}, pages = {358--366}, year = {2015}, editor = {Meila, Marina and Heskes, Tom}, volume = {R13}, series = {Proceedings of Machine Learning Research}, month = {12--16 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r13/main/assets/liu15c/liu15c.pdf}, url = {https://proceedings.mlr.press/r13/liu15c.html}, abstract = {Importance sampling (IS) and its variant, annealed IS (AIS) have been widely used for estimating the partition function in graphical models, such as Markov random fields and deep generative models. However, IS tends to underestimate the partition function and is subject to high variance when the proposal distribution is more peaked than the target distribution. On the other hand, "reverse" versions of IS and AIS tend to overestimate the partition function, and degenerate when the target distribution is more peaked than the proposal distribution. In this work, we present a simple, general method that gives much more reliable and robust estimates than either IS (AIS) or reverse IS (AIS). Our method works by converting the estimation problem into a simple classification problem that discriminates between the samples drawn from the target and the proposal. We give extensive theoretical and empirical justification; in particular, we show that an annealed version of our method significantly outperforms both AIS and reverse AIS as proposed by Burda et al. (2015), which has been the state-of-the-art for likelihood evaluation in deep learning.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Estimating the Partition Function by Discriminance Sampling %A Qiang Liu %A Jian Peng UIUC %A Alexander Ihler %A John Fisher III %B Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2015 %E Marina Meila %E Tom Heskes %F pmlr-vR13-liu15c %I PMLR %P 358--366 %U https://proceedings.mlr.press/r13/liu15c.html %V R13 %X Importance sampling (IS) and its variant, annealed IS (AIS) have been widely used for estimating the partition function in graphical models, such as Markov random fields and deep generative models. However, IS tends to underestimate the partition function and is subject to high variance when the proposal distribution is more peaked than the target distribution. On the other hand, "reverse" versions of IS and AIS tend to overestimate the partition function, and degenerate when the target distribution is more peaked than the proposal distribution. In this work, we present a simple, general method that gives much more reliable and robust estimates than either IS (AIS) or reverse IS (AIS). Our method works by converting the estimation problem into a simple classification problem that discriminates between the samples drawn from the target and the proposal. We give extensive theoretical and empirical justification; in particular, we show that an annealed version of our method significantly outperforms both AIS and reverse AIS as proposed by Burda et al. (2015), which has been the state-of-the-art for likelihood evaluation in deep learning. %Z Reissued by PMLR on 04 October 2026.
APA
Liu, Q., UIUC, J.P., Ihler, A. & III, J.F.. (2015). Estimating the Partition Function by Discriminance Sampling. Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R13:358-366 Available from https://proceedings.mlr.press/r13/liu15c.html. Reissued by PMLR on 04 October 2026.

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