Time-Varying Dynamic Bayesian Networks

Directed graphical models such as Bayesian networks are a favored formalism to model the dependency structures in complex multivariate systems such as those encountered in biology and neural sciences. When the system is undergoing dynamic transformation, often a temporally rewiring network is needed for capturing the dynamic causal influences between covariates. In this paper, we propose a time-varying dynamic Bayesian network (TV-DBN) for modeling the structurally varying directed dependency structures underlying non-stationary biological/neural time series. This is a challenging problem due the non-stationarity and sample scarcity of the time series. We present a kernel reweighted $\ell_1$ regularized auto-regressive procedure for learning the TV-DBN model. Our method enjoys nice properties such as computational efficiency and provable asymptotic consistency. Applying TV-DBN to time series measurements during yeast cell cycle and brain response to visual stimuli reveals interesting dynamics underlying the respective biological systems.