Solving Schrödinger Bridges via Maximum Likelihood

Abstract

The Schrödinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schrödinger bridge remain an active area of research. We prove an equivalence between the SBP and maximum likelihood estimation enabling direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments.

9 pages + appendix (total 28 pages)

Cited by in corpus (4)

• Variational deep learning of equilibrium transition path ensembles
• On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula
• Improving Lunar Topography with Deep Learning Schrödinger Bridges
• Deterministic particle flows for constraining stochastic nonlinear systems