"A
probabilistic approach to exponential convergence of Sinkhorn's algorithm"
Abstract:
The
entropic optimal transport problem (EOT) is obtained adding an entropic regularisation term in the cost function of the Monge-Kantorovich problem and is nowadays regularly employed in machine learning applications as a more tractable and numerically more stable
version of the optimal transport problem. On the other hand, E.Schrödinger asked back in 1931 the question of finding the most likely evolution of a cloud of independent Brownian particles conditionally to observations. The mathematical formulation of his
question through large deviations theory is known as the Schrödinger problem and turns out to be fully equivalent to EOT. In this talk, I shall illustrate both viewpoints and then move on to sketch the ideas of a probabilistic method to show exponential convergence
of Sinkhorn's algorithm, whose application the heart of the recent successful applications of EOT in statistical machine learning and beyond. In particular, we shall discuss how the proposed method opens new perspective for showing exponential convergence
for marginal distribution that are non compactly supported.
We encourage
in-person partecipation. Should you be unable to come, here is the link to the event on Teams:
The seminar is part of the Excellence Project Math@TOV.
You can find a schedule with the next events at the following link: https://www.mat.uniroma2.it/~rds/events.php .