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Title: Random objects: Functional data in nonlinear subspaces and Frechet regression Authors:  Hans-Georg Mueller - University of California Davis (United States) [presenting]
Abstract: Random objects will be illustrated for three commonly encountered scenarios. A general characteristic of random objects is that one has an i.i.d. sample of these objects which lie in a metric space that often has additional properties. The goal is to quantify mean and variation in a sensible way. In the first scenario, functional data that lie on a smooth isometric manifold will be considered. This includes time-warped functional data, where manifold learning with Isomap is shown to provide interpretable data analysis. The second scenario concerns functional data that are density functions. A transformation to a Hilbert space, centered around the Wasserstein mean, then leads to sensible modes of variation. In a third scenario we consider random objects that belong to a more general metric space. We view these as responses in a regression model that features scalar or vector predictors.