Breaking Information Granularity Heterogeneity: A Mutual Information-Inspired Causal Discovery Framework for Multi-Rate Time Series

Causal discovery in multi-rate time series encounters greater challenges compared to regular time series. This stems from a potential problem that has not been noticed and explored in existing studies: information granularity heterogeneity, which refers to the natural difference in information granularity between fast sampling rate data (high information granularity) and slow sampling rate data (low information granularity). Such an imbalance in information granularity can hinder forecasting relationships modeling and induce biased causal learning. Therefore, we propose a Mutual Information-iNspired causal Discovery framework (MIND), aiming to derive rate-agnostic features with consistent information granularity to alleviate information granularity heterogeneity problem. Technically, MIND comprises Stage 1 (pre-training) and Stage 2 (fine-tuning and causal discovery). In Stage 1, empowered by pseudo-slow sampling rate data (generated through the interleaved down sampling strategy) and mutual information, we can eliminate the influence of sampling rates and drive rate-aware encoders (RAEs) to sense key information (i.e., rate-agnostic) that remains unchanged across varying sampling rates. In Stage 2, the well-trained RAEs can extract rate-agnostic features from real multi-rate time series, thus facilitating effective forecasting relationships modeling and yield accurate causal discovery. Empirically, MIND realizes superior performance on various multi-rate scenarios, including four simulation datasets and one real-world dataset.