Open Problem: Learning with Variational Objectives on Measures

06/20/2023

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by   Vivien Cabannes, et al.

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The theory of statistical learning has focused on variational objectives expressed on functions. In this note, we discuss motivations to write similar objectives on measures, in particular to discuss out-of-distribution generalization and weakly-supervised learning. It raises a natural question: can one cast usual statistical learning results to objectives expressed on measures? Does the resulting construction lead to new algorithms of practical interest?