Affine Natural Proximal Learning
Wuchen Li, Alex Tong Lin, and Guido Montúfar
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Submission date: 09. Mar. 2021
Keywords and phrases: optimal transport, information geometry, Proximal operator
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DOI number (of the published article): 10.1007/978-3-030-26980-7_73
We revisit the natural gradient method for learning in statistical manifolds. We consider the proximal formulation and obtain a closed form approximation of the proximity term over an affine subspace of functions in the Legendre dual formulation. We consider two important types of statistical metrics, namely the Wasserstein and Fisher-Rao metrics, and introduce numerical methods for high dimensional parameter spaces.