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Trust-Region Variational Inference with Gaussian Mixture Models

Arenz, Oleg ; Zhong, Mingjun ; Neumann, Gerhard (2022)
Trust-Region Variational Inference with Gaussian Mixture Models.
In: Journal of Machine Learning Research, 2020, 21
doi: 10.26083/tuprints-00022920
Article, Secondary publication, Publisher's Version

Abstract

Many methods for machine learning rely on approximate inference from intractable probability distributions. Variational inference approximates such distributions by tractable models that can be subsequently used for approximate inference. Learning sufficiently accurate approximations requires a rich model family and careful exploration of the relevant modes of the target distribution. We propose a method for learning accurate GMM approximations of intractable probability distributions based on insights from policy search by using information-geometric trust regions for principled exploration. For efficient improvement of the GMM approximation, we derive a lower bound on the corresponding optimization objective enabling us to update the components independently. Our use of the lower bound ensures convergence to a stationary point of the original objective. The number of components is adapted online by adding new components in promising regions and by deleting components with negligible weight. We demonstrate on several domains that we can learn approximations of complex, multimodal distributions with a quality that is unmet by previous variational inference methods, and that the GMM approximation can be used for drawing samples that are on par with samples created by state-of-the-art MCMC samplers while requiring up to three orders of magnitude less computational resources.

Item Type: Article
Erschienen: 2022
Creators: Arenz, Oleg ; Zhong, Mingjun ; Neumann, Gerhard
Type of entry: Secondary publication
Title: Trust-Region Variational Inference with Gaussian Mixture Models
Language: English
Date: 2022
Place of Publication: Darmstadt
Year of primary publication: 2020
Publisher: JMLR
Journal or Publication Title: Journal of Machine Learning Research
Volume of the journal: 21
Collation: 60 Seiten
DOI: 10.26083/tuprints-00022920
URL / URN: https://tuprints.ulb.tu-darmstadt.de/22920
Corresponding Links:
Origin: Secondary publication service
Abstract:

Many methods for machine learning rely on approximate inference from intractable probability distributions. Variational inference approximates such distributions by tractable models that can be subsequently used for approximate inference. Learning sufficiently accurate approximations requires a rich model family and careful exploration of the relevant modes of the target distribution. We propose a method for learning accurate GMM approximations of intractable probability distributions based on insights from policy search by using information-geometric trust regions for principled exploration. For efficient improvement of the GMM approximation, we derive a lower bound on the corresponding optimization objective enabling us to update the components independently. Our use of the lower bound ensures convergence to a stationary point of the original objective. The number of components is adapted online by adding new components in promising regions and by deleting components with negligible weight. We demonstrate on several domains that we can learn approximations of complex, multimodal distributions with a quality that is unmet by previous variational inference methods, and that the GMM approximation can be used for drawing samples that are on par with samples created by state-of-the-art MCMC samplers while requiring up to three orders of magnitude less computational resources.

Uncontrolled Keywords: approximate inference, variational inference, sampling, policy search, mcmc, markov chain monte carlo
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-229205
Classification DDC: 000 Generalities, computers, information > 004 Computer science
Divisions: 20 Department of Computer Science
20 Department of Computer Science > Intelligent Autonomous Systems
Date Deposited: 25 Nov 2022 12:42
Last Modified: 24 May 2023 09:34
PPN: 503637777
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