BIDS Machine Learning and Science Forum
Date: Monday, June 14, 2021
Time: 11:00 AM - 12:00 PM Pacific Time
Location: Participate remotely using this Zoom link
Training stochastic differential equation models using ordinary differential equations
Speaker: Liam Hodgkinson, Statistics, UC Berkeley
Abstract: We provide a general framework for treating models comprised of stochastic differential equations (SDEs) as random ordinary differential equations (ODEs), which can be trained using existing techniques. The approach is based on the celebrated theory of rough paths, which allows the underlying Brownian motion to be treated as a latent variable and approximated. For scalar loss functions, this approach naturally recovers the popular stochastic adjoint method of Li et al. (2020) for training neural SDEs, while supporting a more flexible class of approximations. Furthermore, we show that our framework allows for density estimation of SDEs, enabling “stochastic continuous normalizing flows”, an extension of continuous normalizing flows using SDE models in place of ODEs.
The BIDS Machine Learning and Science Forum meets biweekly to discuss current applications across a wide variety of research domains in the physical sciences and beyond. These active sessions bring together domain scientists, statisticians, and computer scientists who are either developing state-of-the-art methods or are interested in applying these methods in their research. This Forum is organized by BIDS Faculty Affiliate Uroš Seljak (professor of Physics at UC Berkeley), BIDS Research Affiliate Ben Nachman (Physicist at Lawrence Berkeley National Laboratory), Vanessa Böhm and Ben Erichson. All interested members of the UC Berkeley and Berkeley Lab communities are welcome and encouraged to attend. To receive email notifications about upcoming meetings, or to request more information, please contact berkeleymlforum@gmail.com.