Normalizing Constant Estimation with Gaussianized Bridge Sampling

He Jia, Uros Seljak
Proceedings of The 2nd Symposium on Advances in Approximate Bayesian Inference, PMLR 118:1-14, 2020.

Abstract

Normalizing constant (also called partition function, Bayesian evidence, or marginal likelihood) is one of the central goals of Bayesian inference, yet most of the existing methods are both expensive and inaccurate. Here we develop a new approach, starting from posterior samples obtained with a standard Markov Chain Monte Carlo (MCMC). We apply a novel Normalizing Flow (NF) approach to obtain an analytic density estimator from these samples, followed by Optimal Bridge Sampling (OBS) to obtain the normalizing constant. We compare our method which we call Gaussianized Bridge Sampling (GBS) to existing methods such as Nested Sampling (NS) and Annealed Importance Sampling (AIS) on several examples, showing our method is both signicantly faster and substantially more accurate than these methods, and comes with a reliable error estimation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v118-jia20a, title = { Normalizing Constant Estimation with Gaussianized Bridge Sampling}, author = {Jia, He and Seljak, Uros}, booktitle = {Proceedings of The 2nd Symposium on Advances in Approximate Bayesian Inference}, pages = {1--14}, year = {2020}, editor = {Zhang, Cheng and Ruiz, Francisco and Bui, Thang and Dieng, Adji Bousso and Liang, Dawen}, volume = {118}, series = {Proceedings of Machine Learning Research}, month = {08 Dec}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v118/jia20a/jia20a.pdf}, url = {https://proceedings.mlr.press/v118/jia20a.html}, abstract = { Normalizing constant (also called partition function, Bayesian evidence, or marginal likelihood) is one of the central goals of Bayesian inference, yet most of the existing methods are both expensive and inaccurate. Here we develop a new approach, starting from posterior samples obtained with a standard Markov Chain Monte Carlo (MCMC). We apply a novel Normalizing Flow (NF) approach to obtain an analytic density estimator from these samples, followed by Optimal Bridge Sampling (OBS) to obtain the normalizing constant. We compare our method which we call Gaussianized Bridge Sampling (GBS) to existing methods such as Nested Sampling (NS) and Annealed Importance Sampling (AIS) on several examples, showing our method is both signicantly faster and substantially more accurate than these methods, and comes with a reliable error estimation.} }
Endnote
%0 Conference Paper %T Normalizing Constant Estimation with Gaussianized Bridge Sampling %A He Jia %A Uros Seljak %B Proceedings of The 2nd Symposium on Advances in Approximate Bayesian Inference %C Proceedings of Machine Learning Research %D 2020 %E Cheng Zhang %E Francisco Ruiz %E Thang Bui %E Adji Bousso Dieng %E Dawen Liang %F pmlr-v118-jia20a %I PMLR %P 1--14 %U https://proceedings.mlr.press/v118/jia20a.html %V 118 %X Normalizing constant (also called partition function, Bayesian evidence, or marginal likelihood) is one of the central goals of Bayesian inference, yet most of the existing methods are both expensive and inaccurate. Here we develop a new approach, starting from posterior samples obtained with a standard Markov Chain Monte Carlo (MCMC). We apply a novel Normalizing Flow (NF) approach to obtain an analytic density estimator from these samples, followed by Optimal Bridge Sampling (OBS) to obtain the normalizing constant. We compare our method which we call Gaussianized Bridge Sampling (GBS) to existing methods such as Nested Sampling (NS) and Annealed Importance Sampling (AIS) on several examples, showing our method is both signicantly faster and substantially more accurate than these methods, and comes with a reliable error estimation.
APA
Jia, H. & Seljak, U.. (2020). Normalizing Constant Estimation with Gaussianized Bridge Sampling. Proceedings of The 2nd Symposium on Advances in Approximate Bayesian Inference, in Proceedings of Machine Learning Research 118:1-14 Available from https://proceedings.mlr.press/v118/jia20a.html.

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