提出新方法精准度量连续时间序列与离散事件序列的依赖关系。
Estimating Mutual Information between Time Series and Temporal Event Sequences Across Diverse Analysis Tasks
- 不需数据转换，直接建模连续与离散数据的双重特性。
- 在四类任务中均优于现有方法，准确率与稳定性显著提升。
- 适合处理异构时序数据的因果分析、特征选择等场景。
成对依赖度量如相关性和因果关系是时间数据分析的基础，但目前尚无统一且鲁棒的方法来量化异构数据类型之间的依赖性，特别是连续时间序列与离散时间事件序列之间。现有方法依赖于临时变换或对量化、重复值和事件冗余高度敏感的互信息估计器，导致实际结果存在偏差或不稳定。我们提出一种非参数互信息估计器，无需数据变换、学习或人为离散化，直接衡量时间序列与事件序列间的依赖关系。该方法通过建模真实世界时间序列的连续-离散双重性来处理量化和重复值问题，并引入潜在事件聚类策略以缓解事件共现和冗余带来的偏差。结合二者，形成统一且鲁棒的框架，弥合离散与连续互信息的鸿沟。我们在四类代表性任务上进行评估：用于因果分析的离散-连续时延互信息、全局与局部时间重复发现、时间序列预测中的离散协变量选择，以及分类任务中的连续特征选择。在合成与真实数据集上的实验表明，本方法在准确性、鲁棒性和可解释性方面均持续优于现有方法，可作为异构时序数据的通用依赖算子，类似于皮尔逊相关系数在同质时间序列中的地位。代码已公开于：https://github.com/HaojiHu/Multimodal-Temporal-Data-Quantification
原文摘要 · Abstract (English)
Pairwise dependence measures such as correlation and causality are fundamental to temporal data mining, yet there is still no principled and robust way to quantify dependence between heterogeneous data types, especially between continuous time series and discrete temporal event sequences. Existing approaches rely on ad hoc transformations or mutual-information estimators that are highly sensitive to quantization, repeated values, and event redundancy, leading to biased or unstable results in practice. We propose a nonparametric mutual information estimator that directly measures the dependence between time series and event sequences without data transformation, learning, or ad hoc discretization. Our method models the continuous-discrete duality of real-world time series to handle quantization and repeated-value artifacts and introduces a latent event clustering strategy to mitigate bias from event co-occurrence and redundancy. Together, these yield a robust and unified framework that bridges discrete and continuous mutual information. We evaluate the proposed estimator on four representative tasks: discrete-continuous time-delayed mutual information for causality analysis, global and local temporal repetition discovery, discrete covariate selection for time series forecasting, and continuous feature selection for classification. Experiments on synthetic and real-world datasets show consistent improvements over existing methods in accuracy, robustness, and interpretability, positioning our approach as a general-purpose dependence operator for heterogeneous temporal data, similar to Pearson correlation for homogeneous time series. Code available at: https://github.com/HaojiHu/Multimodal-Temporal-Data-Quantification
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