A Markov-switching hidden heterogeneous network autoregressive model for multivariate time series data with multimodality
提出一种新模型，假设每个顶点有多个隐状态并依马尔可夫过程切换，通过异质网络自回归模型融合自身与邻居的隐效应，可纳入外生协变量，用于建模多模态多元时间序列数据。
Multivariate networked time series data are ubiquitous in many applications, where multiple variables of interest are sequentially collected over time for each vertex as multivariate time series. Data of different vertices may have heterogeneous influence on each other through the network topology. These time series may usually exhibit multimodal marginal distributions, due to complex system variations. In this article, we propose a novel approach for such data modeling. In particular, we assume that each vertex has multiple latent states and exhibits state-switching behaviors according to a Markov process. The multivariate time series of each vertex depend on a defined latent effect variable influenced by both its own latent state and the latent effects of its neighbors through a heterogeneous network autoregressive model according to the network topology. Furthermore, the influence of some exogenous covariates on the time series can also be incorporated in the model. Some model properties are discussed, and a variational EM algorithm is proposed for model parameter estimation and state inference. Extensive synthetic experiments and a real-world case study demonstrate the effectiveness and applicability of the proposed model.