Transferable Time-Series Forecasting under Causal Conditional Shift

This paper focuses on the problem of \textcolor{black}{semi-supervised} domain adaptation for time-series forecasting, which is an easily neglected but challenging problem due to the changeable and complex conditional dependencies. In fact, these domain-specific conditional dependencies are mainly led by the data offset, the time lags, and the variant data distribution. In order to cope with this problem, we analyze the variational conditional dependencies in time-series data and consider that the causal structures are stable among different domains, and further raise the causal conditional shift assumption. Enlightened by this assumption, we consider the causal generation process for time-series data and devise an end-to-end model for transferable time-series forecasting. The proposed method can not only discover the cross-domain \textit{Granger Causality} but also address the cross-domain time-series forecasting problem. It can even provide the interpretability of the predicted results to some extent. We further theoretically analyze the superiority of the proposed methods, where the generalization error on the target domain is not only bounded by the empirical risks on the source and target domains but also by the similarity between the causal structures from different domains. Experimental results on both synthetic and real data demonstrate the effectiveness of the proposed method for transferable time-series forecasting.