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State-of-the-art approaches to causal discovery usually assume a fixed underlying causal model. However, it is often the case that causal models vary across domains or subjects, due to possibly omitted factors that affect the quantitative causal effects. As a typical example, causal connectivity in the brain network has been reported to vary across individuals, with significant differences across groups of people, such as autistics and typical controls. In this paper, we develop a unified framework for causal discovery and mechanism-based group identification. In particular, we propose a specific and shared causal model (SSCM), which takes into account the variabilities of causal relations across individuals/groups and leverages their commonalities to achieve statistically reliable estimation. The learned SSCM gives the specific causal knowledge for each individual as well as the general trend over the population. In addition, the estimated model directly provides the group information of each individual. Experimental results on synthetic and real-world data demonstrate the efficacy of the proposed method. 

In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are particularly challenging in such nonstationary environments. In this paper, we study causal discovery and forecasting for nonstationary time series. By exploiting a particular type of state-space model to represent the processes, we show that nonstationarity helps to identify the causal structure, and that forecasting naturally benefits from learned causal knowledge. Specifically, we allow changes in both causal strengths and noise variances in the nonlinear state-space models, which, interestingly, renders both the causal structure and model parameters identifiable. Given the causal model, we treat forecasting as a problem in Bayesian inference in the causal model, which exploits the time-varying property of the data and adapts to new observations in a principled manner. Experimental results on synthetic and real-world data sets demonstrate the efficacy of the proposed methods.