Scalable Gradients and Variational Inference for Stochastic Differential Equations

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Xuechen Li, Ting-Kam Leonard Wong, Ricky T. Q. Chen, David K. Duvenaud ;
Proceedings of The 2nd Symposium on Advances in Approximate Bayesian Inference, PMLR 118:1-28, 2020.

Abstract

We derive reverse-mode (or adjoint) automatic differentiation for solutions of stochastic differential equations (SDEs), allowing time-efficient and constant-memory computation of pathwise gradients, a continuous-time analogue of the reparameterization trick. Specifically, we construct a backward SDE whose solution is the gradient and provide conditions under which numerical solutions converge. We also combine our stochastic adjoint approach with a stochastic variational inference scheme for continuous-time SDE models, allowing us to learn distributions over functions using stochastic gradient descent. Our latent SDE model achieves competitive performance compared to existing approaches on time series modeling.

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