Robust and Scalable SDE Learning: A Functional Perspective

• URL: http://arxiv.org/abs/2110.05167v1
• Date: Mon, 11 Oct 2021 11:36:50 GMT
• Title: Robust and Scalable SDE Learning: A Functional Perspective
• Authors: Scott Cameron, Tyron Cameron, Arnu Pretorius and Stephen Roberts
• Abstract summary: We propose an importance-sampling for probabilities of observations of SDE estimators for the purposes of learning. The proposed method produces lower-variance estimates compared to algorithms based on SDE. This facilitates the effective use of large-scale parallel hardware for massive decreases in time.
• Score: 5.642000444047032
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and other flexible function approximators. Despite these advances, learning remains computationally expensive due to the sequential nature of SDE integrators. In this work, we propose an importance-sampling estimator for probabilities of observations of SDEs for the purposes of learning. Crucially, the approach we suggest does not rely on such integrators. The proposed method produces lower-variance gradient estimates compared to algorithms based on SDE integrators and has the added advantage of being embarrassingly parallelizable. This facilitates the effective use of large-scale parallel hardware for massive decreases in computation time.

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