Home Page

Papers

Submissions

News

Editorial Board

Announcements

Proceedings

Open Source Software

Search

Statistics

Login

Frequenty Asked Questions

Contact Us



RSS Feed

Fast Automatic Smoothing for Generalized Additive Models

Yousra El-Bachir, Anthony C. Davison; 20(173):1−27, 2019.

Abstract

Generalized additive models (GAMs) are regression models wherein parameters of probability distributions depend on input variables through a sum of smooth functions, whose degrees of smoothness are selected by $L_2$ regularization. Such models have become the de-facto standard nonlinear regression models when interpretability and flexibility are required, but reliable and fast methods for automatic smoothing in large data sets are still lacking. We develop a general methodology for automatically learning the optimal degree of $L_2$ regularization for GAMs using an empirical Bayes approach. The smooth functions are penalized by hyper-parameters that are learned simultaneously by maximization of a marginal likelihood using an approximate expectation-maximization algorithm. The latter involves a double Laplace approximation at the E-step, and leads to an efficient M-step. Empirical analysis shows that the resulting algorithm is numerically stable, faster than the best existing methods and achieves state-of-the-art accuracy. For illustration, we apply it to an important and challenging problem in the analysis of extremal data.

[abs][pdf][bib]       
© JMLR 2019. (edit, beta)