Modeling Binary Time Series Using Gaussian Processes with Application to Predicting Sleep States
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Online Publication Date2018-10-02
Print Publication Date2018-10
Permanent link to this recordhttp://hdl.handle.net/10754/631294
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AbstractMotivated by the problem of predicting sleep states, we develop a mixed effects model for binary time series with a stochastic component represented by a Gaussian process. The fixed component captures the effects of covariates on the binary-valued response. The Gaussian process captures the residual variations in the binary response that are not explained by covariates and past realizations. We develop a frequentist modeling framework that provides efficient inference and more accurate predictions. Results demonstrate the advantages of improved prediction rates over existing approaches such as logistic regression, generalized additive mixed model, models for ordinal data, gradient boosting, decision tree and random forest. Using our proposed model, we show that previous sleep state and heart rates are significant predictors for future sleep states. Simulation studies also show that our proposed method is promising and robust. To handle computational complexity, we utilize Laplace approximation, golden section search and successive parabolic interpolation. With this paper, we also submit an R-package (HIBITS) that implements the proposed procedure.
CitationGao X, Shahbaba B, Ombao H (2018) Modeling Binary Time Series Using Gaussian Processes with Application to Predicting Sleep States. Journal of Classification 35: 549–579. Available: http://dx.doi.org/10.1007/s00357-018-9268-8.
SponsorsThe authors thank the anonymous reviewers for providing insightful comments and suggestions. This work was supported in part by grants awards to H. Ombao (NSF DMS 1509023 and NSF MMS 1461543) and B. Shahbaba (NIH R01-AI107034 and NSF DMS1622490).
JournalJournal of Classification