Joint classification and prediction of random curves using heavy‐tailed process functional regression. (April 2023)

• Record Type: Journal Article
• Authors: Cao, Chunzheng; Liu, Xin; Cao, Shuren; Shi, Jian Qing
• Is Part Of: Pattern recognition. Volume 136(2023)
• Publication Date: 2023-04
• Subjects: Functional data analysis -- Outliers -- Heavy-tailed process -- Bayesian estimation -- MCMC; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2022.109213
• Languages: English
• ISSNs: 0031-3203

Abstract

Highlights: A new HPFR model is contributed to jointly perform classification and prediction of time-varying functional data. Two independent heavy-tailed processes are used to yield robust inferences against both magnitude and shape outliers. The new HPFR inherits the advantages of Gaussian process functional regression (GPFR). At the same time, it makes up for the non-robustness of GPFR. A highly efficient MCMC sampling scheme is implemented for the inferences of the HPFR, thanks to a hierarchical expression of the model structure. Abstract: We propose a heavy-tailed process functional regression to jointly perform classification and prediction of time-varying functional data. We use two independent scale mixtures of Gaussian Processes to respectively model random effects and random errors, yielding robust inferences against both magnitude and shape outliers. We classify random curves by posterior predictive probabilities of class labels and offer a weighted prediction of future curve trends. A Bayesian estimation procedure is implemented through an MCMC sampling algorithm. The performance of classification and prediction of the proposed model is evaluated using simulated studies and some real data sets.