Robust, Accurate Stochastic Optimization for Variational Inference

Fuente: arXiv
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Auteurs principaux: Dhaka, Akash Kumar, Catalina, Alejandro, Andersen, Michael Riis, Magnusson, Måns, Huggins, Jonathan H., Vehtari, Aki
Format: Preprint
Publié: 2020
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author Dhaka, Akash Kumar
Catalina, Alejandro
Andersen, Michael Riis
Magnusson, Måns
Huggins, Jonathan H.
Vehtari, Aki
author_facet Dhaka, Akash Kumar
Catalina, Alejandro
Andersen, Michael Riis
Magnusson, Måns
Huggins, Jonathan H.
Vehtari, Aki
contents We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior distribution,(2) the choice of divergence, and (3) the optimization of the variational objective. We show that even in the best-case scenario when the exact posterior belongs to the assumed variational family, common stochastic optimization methods lead to poor variational approximations if the problem dimension is moderately large. We also demonstrate that these methods are not robust across diverse model types. Motivated by these findings, we develop a more robust and accurate stochastic optimization framework by viewing the underlying optimization algorithm as producing a Markov chain. Our approach is theoretically motivated and includes a diagnostic for convergence and a novel stopping rule, both of which are robust to noisy evaluations of the objective function. We show empirically that the proposed framework works well on a diverse set of models: it can automatically detect stochastic optimization failure or inaccurate variational approximation
format Preprint
id arxiv_https___arxiv_org_abs_2009_00666
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Robust, Accurate Stochastic Optimization for Variational Inference
Dhaka, Akash Kumar
Catalina, Alejandro
Andersen, Michael Riis
Magnusson, Måns
Huggins, Jonathan H.
Vehtari, Aki
Machine Learning
Methodology
We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior distribution,(2) the choice of divergence, and (3) the optimization of the variational objective. We show that even in the best-case scenario when the exact posterior belongs to the assumed variational family, common stochastic optimization methods lead to poor variational approximations if the problem dimension is moderately large. We also demonstrate that these methods are not robust across diverse model types. Motivated by these findings, we develop a more robust and accurate stochastic optimization framework by viewing the underlying optimization algorithm as producing a Markov chain. Our approach is theoretically motivated and includes a diagnostic for convergence and a novel stopping rule, both of which are robust to noisy evaluations of the objective function. We show empirically that the proposed framework works well on a diverse set of models: it can automatically detect stochastic optimization failure or inaccurate variational approximation
title Robust, Accurate Stochastic Optimization for Variational Inference
topic Machine Learning
Methodology
url https://arxiv.org/abs/2009.00666