Nonparametric Bayesian sparse graph linear dynamical systems
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Proceedings of the TwentyFirst International Conference on Artificial Intelligence and Statistics, PMLR 84:19521960, 2018.
Abstract
A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the BernoulliPoisson 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 nondynamic state or a dynamic one. A normalgamma construction is used to shrink the energy captured by the nondynamic states, while the dynamic states can be further categorized into live, absorbing, or noiseinjection states, which capture different types of dynamical components of the underlying time series. The stateoftheart performance of SGLDS is demonstrated with experiments on both synthetic and real data.
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