Due to the challenge posed by multi-source and heterogeneous data collected from diverse environments, causal relationships among features can exhibit variations influenced by different time spans, regions, or strategies. This diversity makes a single causal model inadequate for accurately representing complex causal relationships in all observational data, a crucial consideration in causal learning. To address this challenge, the nonlinear Causal Kernel Clustering method is introduced for heterogeneous subgroup causal learning, highlighting variations in causal relationships across diverse subgroups. The main component for clustering heterogeneous subgroups lies in the construction of the $u$-centered sample mapping function with the property of unbiased estimation, which assesses the differences in potential nonlinear causal relationships in various samples and supported by causal identifiability theory. Experimental results indicate that the method performs well in identifying heterogeneous subgroups and enhancing causal learning, leading to a reduction in prediction error.

Time series analysis is a vital task with broad applications in various domains. However, effectively capturing cross-dimension and cross-time dependencies in non-stationary time series poses significant challenges, particularly in the context of environmental factors. The spurious correlation induced by the environment confounds the causal relationships between cross-dimension and cross-time dependencies. In this paper, we introduce a novel framework called Caformer (\underline{\textbf{Ca}}usal Trans\underline{\textbf{former}}) for time series analysis from a causal perspective. Specifically, our framework comprises three components: Dynamic Learner, Environment Learner, and Dependency Learner. The Dynamic Learner unveils dynamic interactions among dimensions, the Environment Learner mitigates spurious correlations caused by environment with a back-door adjustment, and the Dependency Learner aims to infer robust interactions across both time and dimensions. Our Caformer demonstrates consistent state-of-the-art performance across five mainstream time series analysis tasks, including long- and short-term forecasting, imputation, classification, and anomaly detection, with proper interpretability.