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Moment-Based Variational Inference for Stochastic Differential Equations

Wildner, Christian ; Koeppl, Heinz (2022)
Moment-Based Variational Inference for Stochastic Differential Equations.
24th International Conference on Artificial Intelligence and Statistics (AISTATS) 2021. Virtual (13.04.2021-15.04.2021)
doi: 10.26083/tuprints-00021512
Conference or Workshop Item, Secondary publication, Publisher's Version

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Abstract

Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and approximate the posterior by a set of moment functions. In combination with moment closure, the smoothing problem is reduced to a deterministic optimal control problem. Exploiting the path-wise Fisher information, we propose an optimization procedure that corresponds to a natural gradient descent in the variational parameters. Our approach allows for richer variational approximations that extend to state-dependent diffusion terms. The classical Gaussian process approximation is recovered as a special case.

Item Type: Conference or Workshop Item
Erschienen: 2022
Creators: Wildner, Christian ; Koeppl, Heinz
Type of entry: Secondary publication
Title: Moment-Based Variational Inference for Stochastic Differential Equations
Language: English
Date: 2022
Place of Publication: Darmstadt
Year of primary publication: 2021
Publisher: PMLR
Book Title: Proceedings of The 24th International Conference on Artificial Intelligence and Statistics
Series: Proceedings of Machine Learning Research
Series Volume: 130
Event Title: 24th International Conference on Artificial Intelligence and Statistics (AISTATS) 2021
Event Location: Virtual
Event Dates: 13.04.2021-15.04.2021
DOI: 10.26083/tuprints-00021512
URL / URN: https://tuprints.ulb.tu-darmstadt.de/21512
Corresponding Links:
Origin: Secondary publication service
Abstract:

Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and approximate the posterior by a set of moment functions. In combination with moment closure, the smoothing problem is reduced to a deterministic optimal control problem. Exploiting the path-wise Fisher information, we propose an optimization procedure that corresponds to a natural gradient descent in the variational parameters. Our approach allows for richer variational approximations that extend to state-dependent diffusion terms. The classical Gaussian process approximation is recovered as a special case.

Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-215125
Classification DDC: 000 Generalities, computers, information > 004 Computer science
500 Science and mathematics > 510 Mathematics
600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications
18 Department of Electrical Engineering and Information Technology > Self-Organizing Systems Lab
Date Deposited: 20 Jul 2022 13:36
Last Modified: 26 Jul 2022 08:52
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