Recursive Monte Carlo and variational inference with auxiliary variables

Alexander K. Lew, Marco Cusumano-Towner, Vikash K. Mansinghka
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:1096-1106, 2022.

Abstract

A key design constraint when implementing Monte Carlo and variational inference algorithms is that it must be possible to cheaply and exactly evaluate the marginal densities of proposal distributions and variational families. This takes many interesting proposals off the table, such as those based on involved simulations or stochastic optimization. This paper broadens the design space, by presenting a framework for applying Monte Carlo and variational inference algorithms when proposal densities cannot be exactly evaluated. Our framework, recursive auxiliary-variable inference (RAVI), instead approximates the necessary densities using meta-inference: an additional layer of Monte Carlo or variational inference, that targets the proposal, rather than the model. RAVI generalizes and unifies several existing methods for inference with expressive approximating families, which we show correspond to specific choices of meta-inference algorithm, and provides new theory for analyzing their bias and variance. We illustrate RAVI’s design framework and theorems by using them to analyze and improve upon Salimans et al.’s Markov Chain Variational Inference, and to design a novel sampler for Dirichlet process mixtures, achieving state-of-the-art results on a standard benchmark dataset from astronomy and on a challenging datacleaning task with Medicare hospital data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-lew22a, title = {Recursive {M}onte {C}arlo and variational inference with auxiliary variables}, author = {Lew, Alexander K. and Cusumano-Towner, Marco and Mansinghka, Vikash K.}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {1096--1106}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/lew22a/lew22a.pdf}, url = {https://proceedings.mlr.press/v180/lew22a.html}, abstract = {A key design constraint when implementing Monte Carlo and variational inference algorithms is that it must be possible to cheaply and exactly evaluate the marginal densities of proposal distributions and variational families. This takes many interesting proposals off the table, such as those based on involved simulations or stochastic optimization. This paper broadens the design space, by presenting a framework for applying Monte Carlo and variational inference algorithms when proposal densities cannot be exactly evaluated. Our framework, recursive auxiliary-variable inference (RAVI), instead approximates the necessary densities using meta-inference: an additional layer of Monte Carlo or variational inference, that targets the proposal, rather than the model. RAVI generalizes and unifies several existing methods for inference with expressive approximating families, which we show correspond to specific choices of meta-inference algorithm, and provides new theory for analyzing their bias and variance. We illustrate RAVI’s design framework and theorems by using them to analyze and improve upon Salimans et al.’s Markov Chain Variational Inference, and to design a novel sampler for Dirichlet process mixtures, achieving state-of-the-art results on a standard benchmark dataset from astronomy and on a challenging datacleaning task with Medicare hospital data.} }
Endnote
%0 Conference Paper %T Recursive Monte Carlo and variational inference with auxiliary variables %A Alexander K. Lew %A Marco Cusumano-Towner %A Vikash K. Mansinghka %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-lew22a %I PMLR %P 1096--1106 %U https://proceedings.mlr.press/v180/lew22a.html %V 180 %X A key design constraint when implementing Monte Carlo and variational inference algorithms is that it must be possible to cheaply and exactly evaluate the marginal densities of proposal distributions and variational families. This takes many interesting proposals off the table, such as those based on involved simulations or stochastic optimization. This paper broadens the design space, by presenting a framework for applying Monte Carlo and variational inference algorithms when proposal densities cannot be exactly evaluated. Our framework, recursive auxiliary-variable inference (RAVI), instead approximates the necessary densities using meta-inference: an additional layer of Monte Carlo or variational inference, that targets the proposal, rather than the model. RAVI generalizes and unifies several existing methods for inference with expressive approximating families, which we show correspond to specific choices of meta-inference algorithm, and provides new theory for analyzing their bias and variance. We illustrate RAVI’s design framework and theorems by using them to analyze and improve upon Salimans et al.’s Markov Chain Variational Inference, and to design a novel sampler for Dirichlet process mixtures, achieving state-of-the-art results on a standard benchmark dataset from astronomy and on a challenging datacleaning task with Medicare hospital data.
APA
Lew, A.K., Cusumano-Towner, M. & Mansinghka, V.K.. (2022). Recursive Monte Carlo and variational inference with auxiliary variables. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:1096-1106 Available from https://proceedings.mlr.press/v180/lew22a.html.

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