Gaussian process functional regression model for curve prediction and clustering
Seminar Room 2, Newton Institute Gatehouse
In this talk I will first discuss Gaussian Process Functional Regression (GPFR) model, which is used to model functional response curves with a set of functional covariates (the dimension of the covariates may be very large). There are two main features: modelling nonlinear and nonparametric functional regression relationship and modelling covariance structure and mean structure simultaneously. The method gives very accurate results for curve fitting and prediction but side-steps the problem of heterogeneity. I will then discuss how to define a hierarchical mixture model to model 'spatially' indexed functional data, i.e., the heterogeneity is dependent on factors such as region or individual patient's information. The mixture model has also been used for curve clustering, but focusing on the problem of clustering functional relationships between response curve and covariates, i.e. the clustering is based on the surface shape of the functional response against the set of functional covariates. Some applications based on simulated data and real data will be presented.