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

TL;DR

PHAR tackles the interpretability gap in time series classification by converting post-hoc numeric attributions from SHAP and LIME into interval-based rules. It introduces a fusion mechanism to merge rules across explainers (and with Anchor) while optimizing for coverage, confidence, and simplicity, aided by a hyperparameter-tuned numeric-to-rule transformation. The approach is validated on 43 UCR/UEA datasets using a ConvLSTM1D classifier, showing competitive interpretability and fidelity with scalable computation. Visualizations overlay the rules on time series to aid domain experts, addressing Rashomon-style contradictions and providing concise, actionable explanations. Overall, PHAR advances practical, domain-adaptable explainability for TS models and offers a scalable path toward integrated, rules-based interpretations.

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.

Figures (19)

• Figure 1: Rules derived from post-hoc model explanations like SHAP.
• Figure 2: Proposed framework with highlighted research questions RQ1… RQ4.
• Figure 3: Architectural overview of the ConvLSTM1D-based model used in the experiments.
• Figure 4: Critical Difference Diagrams for selected metrics: (a) objective function $\bar{M}$, (b) $\bar{\text{CONF}} \times ER$, (c) $\bar{\text{CONF}}$, (d) $\bar{\text{COV}}$, (e) average feature count $\bar{F(n)}$, (f) explained ratio $ER$. Methods joined by horizontal lines do not differ significantly at $\alpha=0.05$.
• Figure 5: Critical Difference Diagrams for selected metrics using fusion methods: (a) objective function $\bar{M}$, (b) $\bar{\text{CONF}} \times ER$, (c) $\bar{\text{CONF}}$, (d) $\bar{\text{COV}}$, (e) average feature count $\bar{F(n)}$, (f) explained ratio $ER$. Horizontal lines connect methods with no statistically significant differences ($\alpha=0.05$).