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Parameter Estimation of Generalized Linear Models without Assuming their Link Function

Sreangsu Acharyya, Joydeep Ghosh
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, pp. 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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