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Title: A general framework for ID-based data structures to derive erm-approaches for learning Authors:  Julian Gerstenberg - Goethe University Frankfurt (Germany) [presenting]
Abstract: An abstract ID-based data structure is defined as a contravariant functor from the category of finite sets with injections as morphisms to the category of measurable spaces. An abstract framework for ID-based data structures (ID = identifier) using the language of category theory is presented without assuming any knowledge of CT. Many important data structures are instances of the abstract definition: sequential data (data of this type is of the form $x_1,x_2,\dots,x_n$ when using IDs $\{1,\dots,n\}$), partitions, graphs, orders (total, partial,$\dots$), hierarchies, arrays and many more. Within the abstract framework, one can develop a rich exchangeability theory that is of foundational importance to many statistical applications, one of which being empirical risk minimization approaches for statistical learning tasks.