Graph Gamma Process Linear Dynamical Systems

Abstract

We introduce graph gamma process (GGP) linear dynamical systems to model real-valued multivariate time series. GGP generates $S$ latent states that are shared by $K$ different communities, each of which is characterized by its own pattern of activation probabilities imposed on a $S\times S$ directed sparse graph, and allow both $S$ and $K$ to grow without bound. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a parsimonious set of multivariate sub-sequences generated by formed communities. In each sub-sequence, different data dimensions often share similar temporal patterns but may exhibit distinct magnitudes, and hence allowing the superposition of all sub-sequences to exhibit diverse behaviors at different data dimensions. On both synthetic and real-world time series, the proposed nonparametric Bayesian dynamic models, which are initialized at random, consistently exhibit good predictive performance in comparison to a variety of baseline models, revealing interpretable latent state transition patterns and decomposing the time series into distinctly behaved sub-sequences.