Probabilistic dynamic causal model for temporal data

Learning temporal causal structures between time series is one of key tools for analyzing time series data. Most previous works focuse on learning with static temporal causal relationships. However, in many real world applications, such as climate environment and transportation system, the causal structures vary dramatically over time. In this paper, we propose a probabilistic dynamic causal (PDC) model based on Lasso-Granger to uncover the dynamic temporal dependencies. Specifically, the PDC model infers different state varying of temporal data and causal structures of each state in one unified model. We devise the expectation-maximization (EM) algorithm to infer the model parameters. Furthermore, to address the smoothness of state varying in adjacent time, we extend the PDC model with a regularization term encouraging states to be similar in adjacent time. Though it may slightly decrease the precision on training data, it improves the generalization capability of the model. We conduct experiments on synthetic dataset as well as two real-world datasets of climate and traffic to evaluate the effectiveness of the PDC model. Experimental results show that the proposed model is effective in discovering the dynamic causal factors of Particulate Matter 2.5 (PM2.5) and traffic spatial causalities.