Moment-Based Variational Inference for Stochastic Differential Equations

• URL: http://arxiv.org/abs/2103.00988v1
• Date: Mon, 1 Mar 2021 13:20:38 GMT
• Title: Moment-Based Variational Inference for Stochastic Differential Equations
• Authors: Christian Wildner and Heinz Koeppl
• Abstract summary: We construct the variational process as a controlled version of the prior process. We 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.
• Score: 31.494103873662343
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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