Affine Natural Proximal Learning

Wuchen Li, Alex Tong Lin, and Guido Montúfar

Contact the author: Please use for correspondence this email.
Submission date: 09. Mar. 2021
Pages: 11
Bibtex
Keywords and phrases: optimal transport, information geometry, Proximal operator
Download full preprint: PDF (411 kB)
DOI number (of the published article): 10.1007/978-3-030-26980-7_73

Abstract:
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.