Transport information geometry: current and future

Wuchen Li
University of California, Los Angeles (UCLA)

In this talk, I will briefly give an overview of the newly emerged area: transport information geometry. We quickly review information geometry, which emphasizes the geometry of the learning model and theoretical AI, based on invariance concerning transformations of the hypotheses and their parametrization. We formulate the geometry in optimal transport, which departs from the geometry of the data/sample space and relates to math physics equations. We shall apply the information-differential-geometry angle towards optimal transport, named the transport information geometry. Several current developments and future plans will be provided. Many open problems will be given in this direction.

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