Gaussian Process Regression Analysis for Functional Data

This work presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dimensional data and variable selection. They also explore novel nonparametric statistical methods for curve prediction, curve clustering, functional ANOVA, and functional regression analysis of batch data, repeated curves, and non-Gaussian data. Some MATLAB^® and C codes are available on the first author’s website.

Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables.

Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dimensional data and variable selection. The remainder of the text explores advanced topics of functional regression analysis, including novel nonparametric statistical methods for curve prediction, curve clustering, functional ANOVA, and functional regression analysis of batch data, repeated curves, and non-Gaussian data.

Many flexible models based on Gaussian processes provide efficient ways of model learning, interpreting model structure, and carrying out inference, particularly when dealing with large dimensional functional data. This book shows how to use these Gaussian process regression models in the analysis of functional data. Some MATLAB^® and C codes are available on the first author’s website.