Functional additive regression

By Yingying Fan, Gareth M. James, Peter Radchenko. 2015

145 citations recorded by the source corpus.

We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar response, $Y$, in two key respects. First, FAR uses a penalized least squares optimization approach to efficiently deal with high-dimensional problems involving a large number of functional predictors. Second, FAR extends beyond the standard linear regression setting to fit general nonlinear additive models. We demonstrate that FAR can be implemented with a wide range of penalty functions using a highly efficient coordinate descent algorithm. Theoretical results are developed which provide motivation for the FAR optimization criterion. Finally, we show through simulations and two real data sets that FAR can significantly outperform competing methods.

Subfields: Computer Vision and Pattern Recognition, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5f7d9226c7b9f3678547457d684ef066ed2a139c

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Citations in the corpus

Grouped variable importance with random forests and application to multiple functional data analysis (2014, background): “Recently, Matsui and Konishi (2011); Fan and James (2013) have proposed answers to the linear regression problem with Lasso-like penalties.”