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Explanation Space: A New Perspective into Time Series Interpretability

Shahbaz Rezaei, Xin Liu

TL;DR

The paper tackles time-series interpretability by introducing explanation-space projection, enabling post-hoc explanations of models trained in the time domain within alternative spaces such as frequency, time-frequency, min-zero, difference, and SSA decomposition. It formalizes the approach with a reversible representation F, where z = F(x) and M'(z) = M(F^{-1}(z)), so any existing XAI method E can be used in the new space without retraining the model. A bounded sparsity metric Spr and robustness/faithfulness assessments are proposed to compare explanations across spaces, revealing that different time-series types favor different spaces (e.g., AudioMNIST in Time/Freq, FordA in Frequency, ECGs in Difference/Min Zero). The findings highlight practical guidance: select the explanation space based on data characteristics to achieve sparser, more faithful, and potentially more robust explanations, while preserving the model’s predictive behavior. This framework bridges application-agnostic XAI techniques with domain-specific interpretability needs, enabling broader adoption and deeper insights into time-series models.

Abstract

Human understandable explanation of deep learning models is essential for various critical and sensitive applications. Unlike image or tabular data where the importance of each input feature (for the classifier's decision) can be directly projected into the input, time series distinguishable features (e.g. dominant frequency) are often hard to manifest in time domain for a user to easily understand. Additionally, most explanation methods require a baseline value as an indication of the absence of any feature. However, the notion of lack of feature, which is often defined as black pixels for vision tasks or zero/mean values for tabular data, is not well-defined in time series. Despite the adoption of explainable AI methods (XAI) from tabular and vision domain into time series domain, these differences limit the application of these XAI methods in practice. In this paper, we propose a simple yet effective method that allows a model originally trained on the time domain to be interpreted in other explanation spaces using existing methods. We suggest five explanation spaces, each of which can potentially alleviate these issues in certain types of time series. Our method can be easily integrated into existing platforms without any changes to trained models or XAI methods. The code will be released upon acceptance.

Explanation Space: A New Perspective into Time Series Interpretability

TL;DR

The paper tackles time-series interpretability by introducing explanation-space projection, enabling post-hoc explanations of models trained in the time domain within alternative spaces such as frequency, time-frequency, min-zero, difference, and SSA decomposition. It formalizes the approach with a reversible representation F, where z = F(x) and M'(z) = M(F^{-1}(z)), so any existing XAI method E can be used in the new space without retraining the model. A bounded sparsity metric Spr and robustness/faithfulness assessments are proposed to compare explanations across spaces, revealing that different time-series types favor different spaces (e.g., AudioMNIST in Time/Freq, FordA in Frequency, ECGs in Difference/Min Zero). The findings highlight practical guidance: select the explanation space based on data characteristics to achieve sparser, more faithful, and potentially more robust explanations, while preserving the model’s predictive behavior. This framework bridges application-agnostic XAI techniques with domain-specific interpretability needs, enabling broader adoption and deeper insights into time-series models.

Abstract

Human understandable explanation of deep learning models is essential for various critical and sensitive applications. Unlike image or tabular data where the importance of each input feature (for the classifier's decision) can be directly projected into the input, time series distinguishable features (e.g. dominant frequency) are often hard to manifest in time domain for a user to easily understand. Additionally, most explanation methods require a baseline value as an indication of the absence of any feature. However, the notion of lack of feature, which is often defined as black pixels for vision tasks or zero/mean values for tabular data, is not well-defined in time series. Despite the adoption of explainable AI methods (XAI) from tabular and vision domain into time series domain, these differences limit the application of these XAI methods in practice. In this paper, we propose a simple yet effective method that allows a model originally trained on the time domain to be interpreted in other explanation spaces using existing methods. We suggest five explanation spaces, each of which can potentially alleviate these issues in certain types of time series. Our method can be easily integrated into existing platforms without any changes to trained models or XAI methods. The code will be released upon acceptance.
Paper Structure (12 sections, 10 equations, 7 figures, 5 tables)

This paper contains 12 sections, 10 equations, 7 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Explanation Spaces
  5. Evaluation
  6. Evaluation Criteria
  7. Sparsity on Different Spaces
  8. Robustness on Different Spaces
  9. Decomposition Space
  10. Discussion
  11. Appendices
  12. Explanation Space Implementation

Figures (7)

  • Figure 1: DeepLIFT attribution method on FordA and AudioMNIST datasets.
  • Figure 2: DeepLIFT attribution method on ElectricDevices, ECGFiveDays, and GunPoint datasets.
  • Figure 3: Occlusion XAI on a non-stationary dataset.
  • Figure 4: DeepLIFT attribution on a synthetic dataset for the original TS versus the calibrated attribution on the decomposed components.
  • Figure 5: DeepLIFT on ElectricDevices dataset. While the Shannon entropy indicates less complexity for the frequency domain (3.35 versus 3.50), our sparsity metric indicates less complexity for time domain (0.80 versus 0.40).
  • ...and 2 more figures