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Article overview
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The Reflectron: Exploiting geometry for learning generalized linear models | | Nicholas M. Boffi
; Jean-Jacques E. Slotine
; | | Date: |
15 Jun 2020 | | Abstract: | Generalized linear models (GLMs) extend linear regression by generating the
dependent variables through a nonlinear function of a predictor in a
Reproducing Kernel Hilbert Space. Despite nonconvexity of the underlying
optimization problem, the GLM-tron algorithm of Kakade et al. (2011) provably
learns GLMs with guarantees of computational and statistical efficiency. We
present an extension of the GLM-tron to a mirror descent or natural
gradient-like setting, which we call the Reflectron. The Reflectron enjoys the
same statistical guarantees as the GLM-tron for any choice of the convex
potential function $psi$ used to define mirror descent. Central to our
algorithm, $psi$ can be chosen to implicitly regularize the learned model when
there are multiple hypotheses consistent with the data. Our results extend to
the case of multiple outputs with or without weight sharing. We perform our
analysis in continuous-time, leading to simple and intuitive derivations, with
discrete-time implementations obtained by discretization of the continuous-time
dynamics. We supplement our theoretical analysis with simulations on real and
synthetic datasets demonstrating the validity of our theoretical results. | | Source: | arXiv, 2006.8575 | | Services: | Forum | Review | PDF | Favorites | |
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