The time series of vital signs, such as heart rate (HR) and blood pressure (BP), can exhibit complex dynamic behaviors as a result of internally and externally induced changes in the state of the underlying control systems (Peng et al. 1995; Ivanov et al. 1999; Costa et al. 2002). For instance, time series of BP can exhibit oscillations on the order of seconds (e.g., due to the variations in sympathovagal balance), to minutes (e.g., as a consequence of fever, blood loss, or behavioral factors), to hours (e.g., due to humoral variations, sleep-wake cycle, or circadian effects) (Mancia 2012; Parati et al. 2013). A question of interest is whether “similar” dynamical patterns can be automatically identified across a heterogeneous patient cohort, and be used for prognosis of patients' health and progress.
In this work, we present a Bayesian nonparametric switching Markov processes framework with conditionally linear dynamics to learn phenotypic dynamic behaviors from vital sign time series of a patient cohort, and use the learned dynamics to characterize the changing physiological states of patients for critical-care bed-side monitoring (Lehman et al. 2012, 2013, 2014a; Nemati 2012). We assume that although the underlying dynamical system may be nonlinear and nonstationary and the stochastic noise components can be non-Gaussian, the dynamics can be approximated by a collection of linear dynamical systems (Nemati 2012; Nemati et al. 2012). Each such linear “dynamic” (or mode) is a time-dependent rule that describes how the future state of the system evolves from its current state, centered around a given system equilibrium point. Therefore, an ideal algorithm would be able to identify time series segments that follow a “similar” dynamic, and would switch to a different mode upon a change in the state of the underlying system.
We explore several variants of the Bayesian nonparametric approach to discovery of shared dynamics among patients via switching Markov processes: hierarchical Dirichlet process (HDP) autoregressive hidden Markov model (HDP-AR-HMM) (Teh et al. 2006; Fox et al. 2008), an explicit-duration HDP-based hidden semi-Markov model (HDP-AR-HSMM) (Johnson & Willsky 2013a), and the beta process autoregressive HMM (BP-AR-HMM) (Fox 2009; Fox et al. 2009, 2014).