Foundations of Structural Statistics: Topological Statistical Theory
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Topological Statistical Theory, provides the foundation for a new understanding of classical Statistics: Structural Statistics, which emphasizes intrinsically structured model spaces and structure preserving transformations as the central objects and morphisms of respective categories. The resulting language not only turns out to be highly compatible with classical statistical theory, but indeed outperforms it in simplicity and elegance for complicated model spaces. Maybe the most important present showcases for this frameworks are machine-learning and in particular deep-learning. There above it concerns topological-, geometric- as well as algebraic- data analysis, which respectively derive statistical estimations, by the assumption of simplicial complexes, Riemannian manifolds and algebraic varieties.
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