FLEXtime: Filterbank learning to explain time series

TL;DR

FLEXtime addresses the challenge of explaining time-series predictions when salient information resides in the frequency domain. It introduces a filterbank-based approach that decomposes a time series with $L$ bandpass FIR filters and learns a sparse mask over the bands to preserve the model’s output, optimizing $\mathcal{L}_{FLEXtime} = \mathcal{L}_{D} + \lambda \mathcal{L}_R$ with a cross-entropy distortion and a sparsity constraint. A Fourier-domain baseline, FreqMask, is proposed for comparison, using masks on spectral components with a smoothness prior; FLEXtime demonstrates superior faithfulness and robustness across synthetic and real datasets, including sleep staging and audio/biomedical tasks. The work highlights the practical value of frequency-domain explanations, shows that bandwise interpretability can outperform direct spectral masking, and suggests future directions for automatic filterbank design and hybrid time-frequency explanations.

Abstract

State-of-the-art methods for explaining predictions from time series involve learning an instance-wise saliency mask for each time step; however, many types of time series are difficult to interpret in the time domain, due to the inherently complex nature of the data. Instead, we propose to view time series explainability as saliency maps over interpretable parts, leaning on established signal processing methodology on signal decomposition. Specifically, we propose a new method called FLEXtime that uses a bank of bandpass filters to split the time series into frequency bands. Then, we learn the combination of these bands that optimally explains the model's prediction. Our extensive evaluation shows that, on average, FLEXtime outperforms state-of-the-art explainability methods across a range of datasets. FLEXtime fills an important gap in the current time series explainability methodology and is a valuable tool for a wide range of time series such as EEG and audio. Code is available at https://github.com/theabrusch/FLEXtime.

Figures (10)

• Figure 1: Explainability methods that provide explanations (green heatmaps) in the time domain fail to parsimoniously explain time series data if the salient information is localized in the frequency domain.
• Figure 2: Magnitude response of filterbank with $16$ FIR filters with equal bandwidths.
• Figure 3: FLEXtime: FLEXtime uses a filterbank to split the signal into frequency bands of a suitable bandwidth. It then optimizes a mask which chooses the frequency bands that best explains the signal $X$ in terms of the prediction $\hat{y}$ of black box $\mathbf{f}$. $\mathbf{f}$ is only used for inference and thus frozen during optimization.
• Figure 4: Complexity and smoothness of two different saliency maps.
• Figure 5: Examples of explanations (green heatmaps) on a synthetic dataset example.