Parameter Estimation of Generalized Linear Models without Assuming their Link Function

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Sreangsu Acharyya, Joydeep Ghosh ;
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:10-18, 2015.

Abstract

Canonical generalized linear models (GLM) are completely specified by a finite dimensional vector and a monotonically increasing function called the link function. Standard parameter estimation techniques hold the link function fixed and optimizes over the parameter vector. We propose a parameter-recovery facilitating, jointly-convex, regularized loss functional that is optimized globally over the vector as well as the link function, with best rates possible under a first order oracle model. This widens the scope of GLMs to cases where the link function is unknown.

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