A0929
Title: Sinkhorn diffusion and Wasserstein mirror gradient flows
Authors: Nabarun Deb - University of British Columbia, Vancouver (Canada) [presenting]
Abstract: The sequence of marginals obtained from iterations of the Sinkhorn or IPFP algorithm on joint densities converge is proved, under suitable time and parameter scaling and other assumptions, to be an absolutely continuous curve on the Wasserstein space. The limit is an example of the Wasserstein mirror gradient flow, a construction inspired by the Euclidean mirror gradient flows. In the case of Sinkhorn, the gradient is that of relative entropy. The parabolic Monge Ampere PDE provides an equivalent description of this flow, whose connection to Sinkhorn was noticed before by Berman. A Mckean-Vlasov SDE whose marginal distributions give the same flow is constructed; and can be viewed as the mirror analogue of the Langevin diffusion.
