  A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is
proposed to model sequentially observed multivariate data. SGLDS uses the
Bernoulli-Poisson link together with a gamma process to generate an infinite
dimensional sparse random graph to model state transitions. Depending on the
sparsity pattern of the corresponding row and column of the graph affinity
matrix, a latent state of SGLDS can be categorized as either a non-dynamic
state or a dynamic one. A normal-gamma construction is used to shrink the
energy captured by the non-dynamic states, while the dynamic states can be
further categorized into live, absorbing, or noise-injection states, which
capture different types of dynamical components of the underlying time series.
The state-of-the-art performance of SGLDS is demonstrated with experiments on
both synthetic and real data.
