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, 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v38-acharyya15, title = {{Parameter Estimation of Generalized Linear Models without Assuming their Link Function}}, author = {Acharyya, Sreangsu and Ghosh, Joydeep}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {10--18}, year = {2015}, editor = {Lebanon, Guy and Vishwanathan, S. V. N.}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/acharyya15.pdf}, url = {https://proceedings.mlr.press/v38/acharyya15.html}, 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.} }
Endnote
%0 Conference Paper %T Parameter Estimation of Generalized Linear Models without Assuming their Link Function %A Sreangsu Acharyya %A Joydeep Ghosh %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-acharyya15 %I PMLR %P 10--18 %U https://proceedings.mlr.press/v38/acharyya15.html %V 38 %X 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.
RIS
TY - CPAPER TI - Parameter Estimation of Generalized Linear Models without Assuming their Link Function AU - Sreangsu Acharyya AU - Joydeep Ghosh BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-acharyya15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 10 EP - 18 L1 - http://proceedings.mlr.press/v38/acharyya15.pdf UR - https://proceedings.mlr.press/v38/acharyya15.html AB - 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. ER -
APA
Acharyya, S. & Ghosh, J.. (2015). Parameter Estimation of Generalized Linear Models without Assuming their Link Function. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:10-18 Available from https://proceedings.mlr.press/v38/acharyya15.html.

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