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Explainable classification of astronomical uncertain time series

Michael Franklin Mbouopda, Emille E. O. Ishida, Engelbert Mephu Nguifo, Emmanuel Gangler

TL;DR

This work proposes an uncertaintyaware subsequence based model which achieves a classification comparable to that of state-of-the-art methods and is explainable-by-design, giving domain experts the ability to inspect the model and explain its predictions.

Abstract

Exploring the expansion history of the universe, understanding its evolutionary stages, and predicting its future evolution are important goals in astrophysics. Today, machine learning tools are used to help achieving these goals by analyzing transient sources, which are modeled as uncertain time series. Although black-box methods achieve appreciable performance, existing interpretable time series methods failed to obtain acceptable performance for this type of data. Furthermore, data uncertainty is rarely taken into account in these methods. In this work, we propose an uncertaintyaware subsequence based model which achieves a classification comparable to that of state-of-the-art methods. Unlike conformal learning which estimates model uncertainty on predictions, our method takes data uncertainty as additional input. Moreover, our approach is explainable-by-design, giving domain experts the ability to inspect the model and explain its predictions. The explainability of the proposed method has also the potential to inspire new developments in theoretical astrophysics modeling by suggesting important subsequences which depict details of light curve shapes. The dataset, the source code of our experiment, and the results are made available on a public repository.

Explainable classification of astronomical uncertain time series

TL;DR

This work proposes an uncertaintyaware subsequence based model which achieves a classification comparable to that of state-of-the-art methods and is explainable-by-design, giving domain experts the ability to inspect the model and explain its predictions.

Abstract

Exploring the expansion history of the universe, understanding its evolutionary stages, and predicting its future evolution are important goals in astrophysics. Today, machine learning tools are used to help achieving these goals by analyzing transient sources, which are modeled as uncertain time series. Although black-box methods achieve appreciable performance, existing interpretable time series methods failed to obtain acceptable performance for this type of data. Furthermore, data uncertainty is rarely taken into account in these methods. In this work, we propose an uncertaintyaware subsequence based model which achieves a classification comparable to that of state-of-the-art methods. Unlike conformal learning which estimates model uncertainty on predictions, our method takes data uncertainty as additional input. Moreover, our approach is explainable-by-design, giving domain experts the ability to inspect the model and explain its predictions. The explainability of the proposed method has also the potential to inspire new developments in theoretical astrophysics modeling by suggesting important subsequences which depict details of light curve shapes. The dataset, the source code of our experiment, and the results are made available on a public repository.
Paper Structure (13 sections, 1 theorem, 8 equations, 5 figures, 5 tables, 1 algorithm)

This paper contains 13 sections, 1 theorem, 8 equations, 5 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Related works
  4. Uncertain Subsequence Transform Classification
  5. Experiment
  6. The PLAsTiCC dataset
  7. Results
  8. Shapelet-based methods results:
  9. SAST-based methods results:
  10. Ablation study:
  11. Comparison to SOTA:
  12. Explainability:
  13. Conclusion and future directions

Key Result

Theorem 1

The $\epsilon\text{-similar}$ relationship is not transitive.

Figures (5)

  • Figure 1: Uncertain time series illustrations. The x-axis is the timestamp while the y-axis represents the value of the time series at the corresponding timestamp. The red bars represent the uncertainty of the measured value.
  • Figure 2: Two supernova from PLAsTiCC. They look similar in terms of shapes although they are from distinct classes.
  • Figure 3: Local explainability of a Supernova Type Ia (top) and a Core-collapse Supernova Type II (bottom). The y-axis shows the light intensity of the object while the x-axis represent the timestamp.
  • Figure 4: Local explainability of a Core-collapse Supernova Type Ibc by XEM. The y-axis shows the light intensity of the object while the x-axis represent the timestamp.
  • Figure 5: The top $10$ most discriminative subsequences in the PLAsTiCC dataset. The y-axis shows the light intensity of the object while the x-axis represent the timestamp.

Theorems & Definitions (9)

  • Definition 1: Time series
  • Definition 2: Uncertain time series
  • Definition 3: Subsequence
  • Definition 4: Distance
  • Definition 5: Uncertain Euclidean Distance
  • Definition 6: Separator
  • Definition 7: Shapelet
  • Definition 8: $\epsilon$-similarity
  • Theorem 1