Modeling Binary Time Series Using Gaussian Processes with Application to Predicting Sleep States

TL;DR

This paper introduces a Gaussian process-based mixed effects model for binary time series, specifically applied to sleep state prediction, offering improved accuracy over traditional methods and providing an R package for implementation.

Contribution

The paper develops a novel Gaussian process mixed effects model for binary time series with efficient inference, enhancing sleep state prediction accuracy beyond existing models.

Findings

Outperforms logistic regression and other models in prediction accuracy

Identifies previous sleep states and heart rates as significant predictors

Demonstrates robustness through simulation studies

Abstract

Motivated 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.