Modeling count-valued time series has been receiving increasing attention since count time series naturally arise in physical and social domains. Poisson gamma dynamical systems (PGDSs) are newly-developed methods, which can well capture the expressive latent transition structure and bursty dynamics behind count sequences. In particular, PGDSs demonstrate superior performance in terms of data imputation and prediction, compared with canonical linear dynamical system (LDS) based methods. Despite these advantages, PGDS cannot capture the heterogeneous overdispersed behaviours of the underlying dynamic processes. To mitigate this defect, we propose a negative-binomial-randomized gamma Markov process, which not only significantly improves the predictive performance of the proposed dynamical system, but also facilitates the fast convergence of the inference algorithm. Moreover, we develop methods to estimate both factor-structured and graph-structured transition dynamics, which enable us to infer more explainable latent structure, compared with PGDSs. Finally, we demonstrate the explainable latent structure learned by the proposed method, and show its superior performance in imputing missing data and forecasting future observations, compared with the related models.

翻译：计数时间序列建模日益受到关注，因为计数时间序列自然出现在物理和社会领域。泊松伽马动态系统（PGDS）作为新近开发的方法，能够很好地捕捉计数序列背后富有表现力的潜在转移结构和突发动态。与基于经典线性动态系统（LDS）的方法相比，PGDS在数据插补和预测方面表现出更优的性能。尽管具有这些优势，PGDS无法捕捉底层动态过程中的异质过分散行为。为弥补这一缺陷，我们提出了负二项随机伽马马尔可夫过程，它不仅显著提升了所提动态系统的预测性能，还促进了推断算法的快速收敛。此外，我们开发了同时估计因子结构和图结构转移动态的方法，使得相较于PGDS能够推断出更具可解释性的潜在结构。最后，我们展示了所提方法学习到的可解释潜在结构，并证明了其在缺失数据插补和未来观测预测方面相较于相关模型的优越性能。