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
There is a more recent version of this item available. |
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 |
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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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