A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics

• URL: http://arxiv.org/abs/2402.16297v2
• Date: Thu, 23 May 2024 07:21:27 GMT
• Title: A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics
• Authors: Jiahao Wang, Sikun Yang, Heinz Koeppl, Xiuzhen Cheng, Pengfei Hu, Guoming Zhang,
• Abstract summary: A non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time. 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.
• Score: 51.147876395589925
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for dealing with \emph{noisy} and \emph{incomplete} count data. Among these 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 fails to capture the \emph{time-varying} transition dynamics that are commonly observed in real-world count time sequences. To mitigate this gap, 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.

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