A Convex Formulation of Point Process Heartbeat Dynamics using a Gamma Generalized Linear Model

Heartbeat dynamics have been long studied in understanding the cardiovascular and autonomic nervous systems. Traditional methods use windowed time averaging in order to analyze heartbeat data and are unable to capture the fine temporal nature of heartbeat dynamics. In 2005, Barbieri et al., revolutionized the field by introducing a history-dependent Inverse Gaussian (IG) point process model of heartbeat dynamics, which allows for analysis of such data in continuous time. However, one limitation of this approach is that the maximum likelihood estimation problem is non-convex. This thus requires judicious selection of initial conditions for model fitting and leads to longer runtimes. In this paper, we propose a convex formulation of the point process heartbeat dynamics model utilizing a history-dependent Gamma generalized linear model. Using a dataset of human interbeat intervals, we show that this model uniformly outperforms the IG formulation in runtime, and has comparable goodness of fit, as assessed by the Kolmogorov-Smirnov (KS) distance.