The data-driven Schroedinger bridge

Understand

Erwin Schroedinger posed, and to a large extent solved in 1931/32 the problem of finding the most likely random evolution between two continuous probability distributions.

• This article considers this problem in the case when only samples of the two distributions are available.
• A novel iterative procedure is proposed, inspired by Fortet-Sinkhorn type algorithms.
• Since only samples of the marginals are available, the new approach features constrained maximum likelihood estimation in place of the nonlinear boundary couplings, and importance sampling to propagate the functions $\varphi$ and $\hat{\varphi}$ solving the Schroedinger system.