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Explore a 44-minute lecture from the Erwin Schrödinger International Institute's Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" that delves into the generalization of Information Geometry (IG) and Optimal Transport (OT) distances for Gaussian measures and processes. Learn how regularization in both Entropic 2-Wasserstein distance and Fisher-Rao distance settings leads to dimension-independent convergence and sample complexity. Discover the mathematical framework connecting IG and OT with Gaussian processes and reproducing kernel Hilbert spaces (RKHS), featuring practical closed-form expressions and numerical experiments. Gain insights into these concepts' applications in machine learning and statistics, demonstrated through computational examples with Gaussian processes.
