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| In this talk I will present the framework of optimal information transport (OIT) and the connection to the Fisher-Rao information metric. I will focus on the underlying infinite dimensional Riemannian geometry, and compare it with the geometry of optimal mass transport (OMT) and the Wasserstein $L^2$ distance, as described by Otto (2001). There are similarities and dissimilarities between OMT and OIT: the "lifting equations" in both frameworks involve PDEs, it is non-linear in the former (the Monge-Ampere equation) and linear in the latter (the Poisson equation). I will discuss some applications currently employing OMT, where OIT might be an alternative. Since the lifting PDE for OIT is linear, one can expect significantly faster simulation algorithms. |
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