Functional additive regression
TLDR
Functional Additive Regression uses a penalized least squares optimization approach to efficiently deal with high-dimensional problems involving a large number of functional predictors and can significantly outperform competing methods.Abstract:
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.read more
Citations
More filters
Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling
TL;DR: Using singular value decomposition in transforming genome-wide expression data from genes x arrays space to reduced diagonalized "eigengenes" x "eigenarrays" space gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype.
Journal ArticleDOI
Empirical Processes in M-Estimation
TL;DR: In this article, empirical processes in M-Estimation are studied. But they do not consider the effect of M-values on the accuracy of the M-estimation process.
Posted Content
Functional Regression
TL;DR: Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid.
Journal ArticleDOI
A survey of functional principal component analysis
TL;DR: A review of functional principal component analysis, and its use in explanatory analysis, modeling and forecasting, and classification of functional data is provided in this article from both methodological and practical viewpoints.
Journal ArticleDOI
Methods for scalar-on-function regression
TL;DR: Some of the main approaches to how to fit regression models with scalar responses and functional data points as predictors are reviewed, categorizing the basic model types as linear, nonlinear and nonparametric.
References
More filters
Journal ArticleDOI
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Jianqing Fan,Runze Li +1 more
TL;DR: In this article, penalized likelihood approaches are proposed to handle variable selection problems, and it is shown that the newly proposed estimators perform as well as the oracle procedure in variable selection; namely, they work as well if the correct submodel were known.
Journal ArticleDOI
Model selection and estimation in regression with grouped variables
Ming Yuan,Yi Lin +1 more
TL;DR: In this paper, instead of selecting factors by stepwise backward elimination, the authors focus on the accuracy of estimation and consider extensions of the lasso, the LARS algorithm and the non-negative garrotte for factor selection.
Book
Spline Functions: Basic Theory
TL;DR: The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences.
Journal ArticleDOI
A Statistical View of Some Chemometrics Regression Tools
TL;DR: In this article, the authors examined partial least squares and principal components regression from a statistical perspective and compared them with other statistical methods intended for those situations, such as variable subset selection and ridge regression.
Journal ArticleDOI
Sliced Inverse Regression for Dimension Reduction
TL;DR: In this article, sliced inverse regression (SIR) is proposed to reduce the dimension of the input variable without going through any parametric or nonparametric model-fitting process.