Bayesian Smoothing and Classification of Sparse Functional Data Using Gaussian Process

• Activity Number: 254 - Contributed Poster Presentations: Section on Bayesian Statistical Science
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Tahmidul Islam* and Paramita Chakraborty and James Lynch and John Grego
• Companies: University of South Carolina and University of South Carolina and University of South Carolina and University of South Carolina
• Keywords: Classification; Functional Data; Gaussian Process

Abstract

While sparse observed functional data (FD) is not uncommon in practice, it is often challenging to analyze such data compared to regular functional data. We propose an approach that incorporates the Gaussian process (GP) prior and the mean and the covariance at given test points are obtained from a posterior distribution. The GP prior hyperparameters are estimated by maximizing the marginal likelihood. This Bayesian nonparametric approach is flexible and fully tractable with a wide range of choices for the covariance kernel, inducing function space with different characteristics. The posterior distribution can then be used to classify sparse FD adopting discriminant analysis approach. Performance of this methodology is shown using simulation and real data examples.