Explaining Time Series Classifiers with PHAR: Rule Extraction and Fusion from Post-hoc Attributions

Abstract

Explaining machine learning (ML) models for time series (TS) classification remains challenging due to the difficulty of interpreting raw time series and the high dimensionality of the input space. We introduce PHAR-Post-hoc Attribution Rules - a unified framework that transforms numeric feature attributions from post-hoc, instance-wise explainers (e.g., LIME, SHAP) into structured, human-readable rules. These rules define human-readable intervals that indicate where and when decision-relevant segments occur and can enhance model transparency by localizing threshold-based conditions on the raw series. PHAR performs comparably to native rule-based methods, such as Anchor, while scaling more efficiently to long TS sequences and achieving broader instance coverage. A dedicated rule fusion step consolidates rule sets using strategies like weighted selection and lasso-based refinement, balancing key quality metrics: coverage, confidence, and simplicity. This fusion ensures each instance receives a concise and unambiguous rule, improving both explanation fidelity and consistency. We further introduce visualization techniques to illustrate specificity-generalization trade-offs in the derived rules. PHAR resolves conflicting and overlapping explanations - a common effect of the Rashomon phenomenon - into coherent, domain-adaptable insights. Comprehensive experiments on UCR/UEA Time Series Classification Archive demonstrate that PHAR may improve interpretability, decision transparency, and practical applicability for TS classification tasks by providing concise, human-readable rules aligned with model predictions.