Nonparametric Bayesian Sparse Graph Linear Dynamical Systems
This work addresses the problem of modeling complex time series data for researchers in machine learning and statistics, representing an incremental improvement with a novel method for sparse graph modeling.
The paper tackles modeling sequentially observed multivariate data by proposing a nonparametric Bayesian sparse graph linear dynamical system (SGLDS), which uses a Bernoulli-Poisson link and gamma process to generate infinite-dimensional sparse graphs for state transitions, achieving state-of-the-art performance in experiments on synthetic and real data.
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.