OT at scale: Careful Initialization, Low-rank considerations and Neural Networks
speaker: Marco Cuturi (CREST - ENSAE, Institut Polytechnique de Paris and Apple ML Reseach)abstract: I will present in this talk a series of efforts targeted at increasing the scalability and applicability of OT computations. I will present efforts on two fronts: In the first part, I will discuss speeding up the discrete resolution of the Kantorovich problem, using either the Sinkhorn approach, and, in that case, focusing on efficient heuristics to initialize Sinkhorn potentials, or, alternatively, by parameterizing OT couplings as a product of low-rank non-negative matrices. In the second part I will explain how a parameterization, in the 2-Wasserstein setting, of dual potentials as input-convex neural networks has opened several research avenues, and demonstrate this by illustrating an application to the "inverse JKO" problem, in which my goal is to reconstruct an energy landscape for measures that reconstructs a given population dynamic, an another to the simultaneous and joint estimation of several Monge maps linked by a common set of parameters.
timetable:
Tue 25 Oct, 9:45 - 10:30, Aula Magna Bruno Pontecorvo
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