Graduate Student / Postdoc Seminar

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Plug-in estimation of Schrödinger bridges

Speaker: Jonathan Niles-Weed, Courant Institute and Center for Data Science, New York University

Location: Warren Weaver Hall 1302

Date: Friday, February 7, 2025, 12:30 p.m.

Synopsis:

We propose a procedure for estimating the Schrrödinger bridge between two probability distributions. Unlike existing approaches, our method does not require iteratively simulating forward and backward diffusions or training neural networks to fit unknown drifts. Instead, we show that the potentials obtained from solving the static entropic optimal transport problem between the source and target samples can be modified to yield a natural plug-in estimator of the time-dependent drift that defines the bridge between two measures. Under minimal assumptions, we show that our proposal, which we call the Sinkhorn bridge, provably estimates the Schrrödinger bridge with a rate of convergence that depends on the intrinsic dimensionality of the target measure. Our approach combines results from the areas of sampling, and theoretical and statistical entropic optimal transport. Based on joint work with Aram-Alexandre Pooladian.