A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914806314827776 |
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| author | Wang, Jiahao Yang, Sikun Koeppl, Heinz Cheng, Xiuzhen Hu, Pengfei Zhang, Guoming |
| author_facet | Wang, Jiahao Yang, Sikun Koeppl, Heinz Cheng, Xiuzhen Hu, Pengfei Zhang, Guoming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16297 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics Wang, Jiahao Yang, Sikun Koeppl, Heinz Cheng, Xiuzhen Hu, Pengfei Zhang, Guoming Machine Learning Artificial Intelligence 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. |
| title | A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2402.16297 |