Explaining deep learning models operating on time series data is crucial in various applications of interest which require interpretable and transparent insights from time series signals. In this work, we investigate this problem from an information theoretic perspective and show that most existing measures of explainability may suffer from trivial solutions and distributional shift issues. To address these issues, we introduce a simple yet practical objective function for time series explainable learning. The design of the objective function builds upon the principle of information bottleneck (IB), and modifies the IB objective function to avoid trivial solutions and distributional shift issues. We further present TimeX++, a novel explanation framework that leverages a parametric network to produce explanation-embedded instances that are both in-distributed and label-preserving. We evaluate TimeX++ on both synthetic and real-world datasets comparing its performance against leading baselines, and validate its practical efficacy through case studies in a real-world environmental application. Quantitative and qualitative evaluations show that TimeX++ outperforms baselines across all datasets, demonstrating a substantial improvement in explanation quality for time series data. The source code is available at \url{https://github.com/zichuan-liu/TimeXplusplus}.

翻译：解释在时间序列数据上运行的深度学习模型在需要从时间序列信号中获得可解释且透明洞察的各种应用场景中至关重要。本文从信息论视角研究该问题，并表明现有的大多数可解释性度量可能面临平凡解和分布偏移问题。为解决这些问题，我们提出了一种简单而实用的目标函数用于时间序列可解释学习。该目标函数的设计基于信息瓶颈（IB）原理，并通过对IB目标函数进行修正以避免平凡解和分布偏移问题。我们进一步提出了TimeX++，一种新颖的解释框架，利用参数化网络生成兼具分布内保持和标签保持特性的嵌入解释的实例。我们在合成数据集和真实数据集上评估了TimeX++，将其性能与主流基线方法进行对比，并通过真实环境应用中的案例研究验证其实际有效性。定量与定性评估表明，TimeX++在所有数据集上均优于基线方法，显著提升了时间序列数据的解释质量。源代码见\url{https://github.com/zichuan-liu/TimeXplusplus}。