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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. (Publisher's Version)
In: Proceedings of Machine Learning Research, 130, In: Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, pp. 1918-1926,
Darmstadt, PMLR, 24th International Conference on Artificial Intelligence and Statistics (AISTATS) 2021, Virtual, 13.-15.04.2021, DOI: 10.26083/tuprints-00021512,
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Item Type: Conference or Workshop Item
Origin: Secondary publication service
Status: Publisher's Version
Title: Moment-Based Variational Inference for Stochastic Differential Equations
Language: English
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.

Book Title: Proceedings of The 24th International Conference on Artificial Intelligence and Statistics
Series: Proceedings of Machine Learning Research
Series Volume: 130
Place of Publication: Darmstadt
Publisher: PMLR
Classification DDC: 000 Allgemeines, Informatik, Informationswissenschaft > 004 Informatik
500 Naturwissenschaften und Mathematik > 510 Mathematik
600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
18 Department of Electrical Engineering and Information Technology > Self-Organizing Systems Lab
Event Title: 24th International Conference on Artificial Intelligence and Statistics (AISTATS) 2021
Event Location: Virtual
Event Dates: 13.-15.04.2021
Date Deposited: 20 Jul 2022 13:36
Last Modified: 20 Jul 2022 13:36
DOI: 10.26083/tuprints-00021512
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-215125
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/21512
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