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.
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