Poisson-Gamma Dynamical Systems with Non-Stationary Transition Dynamics
Jiahao Wang Sikun Yang Heinz Koeppl Xiuzhen Cheng Pengfei Hu Guoming Zhang
Bayesian methodologies for handling count-valued time series have gained
prominence due to their ability to infer interpretable latent structures and to
estimate uncertainties, and thus are especially suitable for dealing with noisy
and incomplete count data. Among these Bayesian models, Poisson-Gamma Dynamical
Systems (PGDSs) are proven to be effective in capturing the evolving dynamics
underlying observed count sequences. However, the state-of-the-art PGDS still
falls short in capturing the time-varying transition dynamics that are commonly
observed in real-world count time series. To mitigate this limitation, a
non-stationary PGDS is proposed to allow the underlying transition matrices to
evolve over time, and the evolving transition matrices are modeled by
sophisticatedly-designed Dirichlet Markov chains. Leveraging
Dirichlet-Multinomial-Beta data augmentation techniques, a fully-conjugate and
efficient Gibbs sampler is developed to perform posterior simulation.
Experiments show that, in comparison with related models, the proposed
non-stationary PGDS achieves improved predictive performance due to its
capacity to learn non-stationary dependency structure captured by the
time-evolving transition matrices.