Moment-Based Variational Inference for Stochastic Differential Equations

Christian Wildner, Heinz Koeppl
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1918-1926, 2021.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-wildner21a, title = { Moment-Based Variational Inference for Stochastic Differential Equations }, author = {Wildner, Christian and Koeppl, Heinz}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1918--1926}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/wildner21a/wildner21a.pdf}, url = {https://proceedings.mlr.press/v130/wildner21a.html}, 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. } }
Endnote
%0 Conference Paper %T Moment-Based Variational Inference for Stochastic Differential Equations %A Christian Wildner %A Heinz Koeppl %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-wildner21a %I PMLR %P 1918--1926 %U https://proceedings.mlr.press/v130/wildner21a.html %V 130 %X 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.
APA
Wildner, C. & Koeppl, H.. (2021). Moment-Based Variational Inference for Stochastic Differential Equations . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1918-1926 Available from https://proceedings.mlr.press/v130/wildner21a.html.

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