Regression analysis for a functional response
Technometrics
Hierarchical Gaussian process mixtures for regression
Statistics and Computing
Maximum likelihood ratio test for the stability of sequence of Gaussian random processes
Computational Statistics & Data Analysis
An efficient EM approach to parameter learning of the mixture of gaussian processes
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part II
Some research on functional data analysis
ICSI'10 Proceedings of the First international conference on Advances in Swarm Intelligence - Volume Part II
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Shi, Wang, Murray-Smith and Titterington (Biometrics 63:714---723, 2007) proposed a Gaussian process functional regression (GPFR) model to model functional response curves with a set of functional covariates. Two main problems are addressed by their method: modelling nonlinear and nonparametric regression relationship and modelling covariance structure and mean structure simultaneously. The method gives very good results for curve fitting and prediction but side-steps the problem of heterogeneity. In this paper we present a new method for modelling functional data with `spatially' indexed data, i.e., the heterogeneity is dependent on factors such as region and individual patient's information. For data collected from different sources, we assume that the data corresponding to each curve (or batch) follows a Gaussian process functional regression model as a lower-level model, and introduce an allocation model for the latent indicator variables as a higher-level model. This higher-level model is dependent on the information related to each batch. This method takes advantage of both GPFR and mixture models and therefore improves the accuracy of predictions. 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. The model is examined on simulated data and real data.