Solving Schrödinger Bridges via Maximum Likelihood
This work provides a scalable method for solving Schrödinger bridges, which is incremental as it builds on existing theory but offers practical improvements for applications in machine learning.
The authors tackled the problem of estimating Schrödinger bridges, which are used in machine learning for tasks like dataset alignment, by proving an equivalence to maximum likelihood estimation and proposing a numerical procedure using Gaussian processes, demonstrating its effectiveness in simulations and experiments.
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.