Time is Not Enough: Time-Frequency based Explanation for Time-Series Black-Box Models

TL;DR

This work addresses the limited scope of time-domain explanations for time-series classifiers by introducing SpectralX, a plug-and-play framework that yields time-frequency explanations via STFT and ISTFT while remaining model-agnostic to black-box classifiers. Central to SpectralX is Feature Importance Approximations (FIA), a family of perturbation-based methods (Insertion, Deletion, Combined) that produce class-specific explanations with improved efficiency. Extensive experiments on synthetic data and nine UCR datasets demonstrate that time-frequency explanations generally outperform time-domain explanations, with the FIA Combined method delivering the best overall faithfulness and robustness and receiving strong support from user studies. The framework’s practical impact lies in enabling scalable, interpretable analysis of diverse time-series models across domains, with potential extensions to NLP and CV. Key contributions include (i) SpectralX as a general, plug-in XAI framework for time-series models, (ii) FIA as an efficient, class-specific perturbation approach, and (iii) empirical evidence showing the superiority of time-frequency explanations, especially in the TF domain.

Abstract

Despite the massive attention given to time-series explanations due to their extensive applications, a notable limitation in existing approaches is their primary reliance on the time-domain. This overlooks the inherent characteristic of time-series data containing both time and frequency features. In this work, we present Spectral eXplanation (SpectralX), an XAI framework that provides time-frequency explanations for time-series black-box classifiers. This easily adaptable framework enables users to "plug-in" various perturbation-based XAI methods for any pre-trained time-series classification models to assess their impact on the explanation quality without having to modify the framework architecture. Additionally, we introduce Feature Importance Approximations (FIA), a new perturbation-based XAI method. These methods consist of feature insertion, deletion, and combination techniques to enhance computational efficiency and class-specific explanations in time-series classification tasks. We conduct extensive experiments in the generated synthetic dataset and various UCR Time-Series datasets to first compare the explanation performance of FIA and other existing perturbation-based XAI methods in both time-domain and time-frequency domain, and then show the superiority of our FIA in the time-frequency domain with the SpectralX framework. Finally, we conduct a user study to confirm the practicality of our FIA in SpectralX framework for class-specific time-frequency based time-series explanations. The source code is available in https://github.com/gustmd0121/Time_is_not_Enough

Figures (9)

• Figure 1: Example of the time-domain explanation, where the important regions are overlapping for both classes. In time-frequency domain explanation, however, zero-masking the red-box, which indicates important region in the time-frequency domain, appears as the red region in original time-domain which explains the most important feature of the class.
• Figure 2: (Top) SpectralX Framework and Feature Importance Approximations (FIA). The raw signals are converted to time-frequency representations with Short-Time Fourier Transform(STFT), and a single perturbation-based XAI method is used to generate perturbation outputs. After reverting to perturbed time signal with Inverse STFT, the classifier determines probability scores to determine important class-specific time-frequency features. (Bottom) The three perturbation-based XAI methods represent our FIA. The Insertion method introduces significant features into RBP (Realistic Background Perturbation), a global property of the signal, the Deletion method removes significant features from the original signal, and the Combined method merges the two methods. Numeric values represent increase or decrease in class probability for each method.
• Figure 3: Samples from synthetic dataset for each class. Time and Time-Frequency representation of each sample.
• Figure 4: Human evaluation results
• Figure 5: Explanation samples for Arrowhead dataset, Class 1, Sample 69