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Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes
Anton Mallasto · Aasa Feragen

Mon Dec 04 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #219

We introduce a novel framework for statistical analysis of populations of non- degenerate Gaussian processes (GPs), which are natural representations of uncertain curves. This allows inherent variation or uncertainty in function-valued data to be properly incorporated in the population analysis. Using the 2-Wasserstein metric we geometrize the space of GPs with L2 mean and covariance functions over compact index spaces. We prove existence and uniqueness of the barycenter of a population of GPs, as well as convergence of the metric and the barycenter of their finite-dimensional counterparts. This justifies practical computations. Finally, we demonstrate our framework through experimental validation on GP datasets representing brain connectivity and climate development. A MATLAB library for relevant computations will be published at https://sites.google.com/view/ antonmallasto/software.

Author Information

Anton Mallasto (University of Copenhagen)
Aasa Feragen (University of Copenhagen)