Solving Schr\"odinger Bridges via Maximum Likelihood

Understand

The Schr\"odinger 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 Schr\"odinger 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.