Title: Quantifying Mutual Information in Time Series and Temporal Event Sequences for a Wide Range of Analytical Tasks

Abstract:

While pairwise dependence metrics like correlation and causality are foundational to temporal data mining, the field currently lacks a rigorous and resilient method for measuring dependencies between heterogeneous data modalities—specifically, the interaction between continuous time series and discrete temporal event sequences. Current techniques often depend on arbitrary transformations or mutual information estimators that are prone to bias and instability due to their high sensitivity to quantization, duplicate values, and event redundancy.

To address these limitations, we introduce a nonparametric mutual information estimator designed to assess dependence directly between time series and event sequences. This approach eliminates the need for data transformation, machine learning models, or arbitrary discretization. By modeling the inherent continuous-discrete duality of real-world time series, our method effectively neutralizes artifacts arising from quantization and repeated values. Furthermore, it employs a latent event clustering strategy to reduce bias caused by event co-occurrence and redundancy. These innovations combine to form a robust, unified framework that seamlessly connects discrete and continuous mutual information.

We validated the proposed estimator across four key applications: causality analysis via discrete-continuous time-delayed mutual information, discovery of global and local temporal repetitions, discrete covariate selection for time series forecasting, and continuous feature selection for classification. Empirical results from both synthetic and real-world datasets demonstrate that our method consistently outperforms existing techniques in terms of accuracy, robustness, and interpretability. Consequently, this approach serves as a general-purpose dependence operator for heterogeneous temporal data, analogous to the role of Pearson correlation in homogeneous time series analysis.

Code repository: https://github.com/HaojiHu/Multimodal-Temporal-Data-Quantification

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC