具有时变转移动力学的泊松-伽马动力系统
Poisson-Gamma Dynamical Systems with Time-varying Transition Dynamics
浏览论文内容
中文总结 AI 辅助
本文针对现有泊松-伽马动力系统（PGDS）无法捕捉计数时间序列时变转移动力学的局限，提出TV-PGDS模型，构建三类狄利克雷马尔可夫链，开发高效吉布斯采样器，实验证实其预测性能优于相关模型。
中文摘要 AI 辅助
用于处理计数值时间序列的贝叶斯方法因能够推断可解释的隐结构并估计不确定性而受到关注。在这些贝叶斯模型中，泊松-伽马动力系统（PGDS）被证明能有效捕捉观测计数序列背后的演化动力学。然而，最先进的PGDS仍无法捕捉现实世界计数时间序列中常见的转移动力学。为缓解这一局限，本文提出一种具有时变转移核的PGDS（TV-PGDS），使潜在转移矩阵能随时间演化。研究构建了三种专门设计的狄利克雷马尔可夫链（Dir-Dir、Dir-Gam-Dir、PR-Gam-Dir），以适应这些依赖关系中的异质结构突变。利用狄利克雷-多项分布-贝塔数据增强技术，开发了一种完全共轭且高效的吉布斯采样器用于后验模拟。实验表明，与相关模型相比，所提出的PGDS因能学习随时间演化的转移矩阵所捕捉的时变依赖结构，而实现了更好的预测性能。
英文摘要
Bayesian methodologies for handling count-valued time series have gained prominence due to their ability to infer interpretable latent structures and to estimate uncertainties. 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 transition dynamics that are commonly observed in real-world count time series. To mitigate this limitation, a PGDS with time-varying transition kernel (TV-PGDS), is proposed to allow the underlying transition matrices to evolve over time. Three specifically-designed Dirichlet Markov chains (Dir-Dir, Dir-Gam-Dir, PR-Gam-Dir) are constructed to accommodate heterogeneous structural mutations within these dependencies. 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 PGDS achieves improved predictive performance due to its capacity to learn time-varying dependency structure captured by the time-evolving transition matrices.
发表机构
- University of Arizona（亚利桑那大学）
- Great Bay University（大湾区大学）
- Tsinghua University（清华大学）
机构由 AI 辅助整理，请以论文原文为准。
