Nonparametric Bayesian Sparse Graph Linear Dynamical Systems.

A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) isproposed to model sequentially observed multivariate data. SGLDS uses theBernoulli-Poisson link together with a gamma process to generate an infinitedimensional sparse random graph to model state transitions. Depending on thesparsity pattern of the corresponding row and column of the graph affinitymatrix, a latent state of SGLDS can be categorized as either a non-dynamicstate or a dynamic one. A normal-gamma construction is used to shrink theenergy captured by the non-dynamic states, while the dynamic states can befurther categorized into live, absorbing, or noise-injection states, whichcapture different types of dynamical components of the underlying time series.The state-of-the-art performance of SGLDS is demonstrated with experiments onboth synthetic and real data.