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Towards Accurate and Interpretable Time-series Forecasting: A Polynomial Learning Approach

Bo Liu, Shao-Bo Lin, Changmiao Wang, Xiaotong Liu

TL;DR

The interpretable polynomial learning (IPL) method is proposed, which integrates interpretability into the model structure by explicitly modeling original features and their interactions of arbitrary order through polynomial representations and offers a flexible trade-off between prediction accuracy and interpretability by adjusting the polynomial degree.

Abstract

Time series forecasting enables early warning and has driven asset performance management from traditional planned maintenance to predictive maintenance. However, the lack of interpretability in forecasting methods undermines users' trust and complicates debugging for developers. Consequently, interpretable time-series forecasting has attracted increasing research attention. Nevertheless, existing methods suffer from several limitations, including insufficient modeling of temporal dependencies, lack of feature-level interpretability to support early warning, and difficulty in simultaneously achieving the accuracy and interpretability. This paper proposes the interpretable polynomial learning (IPL) method, which integrates interpretability into the model structure by explicitly modeling original features and their interactions of arbitrary order through polynomial representations. This design preserves temporal dependencies, provides feature-level interpretability, and offers a flexible trade-off between prediction accuracy and interpretability by adjusting the polynomial degree. We evaluate IPL on simulated and Bitcoin price data, showing that it achieves high prediction accuracy with superior interpretability compared with widely used explainability methods. Experiments on field-collected antenna data further demonstrate that IPL yields simpler and more efficient early warning mechanisms.

Towards Accurate and Interpretable Time-series Forecasting: A Polynomial Learning Approach

TL;DR

The interpretable polynomial learning (IPL) method is proposed, which integrates interpretability into the model structure by explicitly modeling original features and their interactions of arbitrary order through polynomial representations and offers a flexible trade-off between prediction accuracy and interpretability by adjusting the polynomial degree.

Abstract

Time series forecasting enables early warning and has driven asset performance management from traditional planned maintenance to predictive maintenance. However, the lack of interpretability in forecasting methods undermines users' trust and complicates debugging for developers. Consequently, interpretable time-series forecasting has attracted increasing research attention. Nevertheless, existing methods suffer from several limitations, including insufficient modeling of temporal dependencies, lack of feature-level interpretability to support early warning, and difficulty in simultaneously achieving the accuracy and interpretability. This paper proposes the interpretable polynomial learning (IPL) method, which integrates interpretability into the model structure by explicitly modeling original features and their interactions of arbitrary order through polynomial representations. This design preserves temporal dependencies, provides feature-level interpretability, and offers a flexible trade-off between prediction accuracy and interpretability by adjusting the polynomial degree. We evaluate IPL on simulated and Bitcoin price data, showing that it achieves high prediction accuracy with superior interpretability compared with widely used explainability methods. Experiments on field-collected antenna data further demonstrate that IPL yields simpler and more efficient early warning mechanisms.
Paper Structure (18 sections, 16 equations, 11 figures, 5 tables, 1 algorithm)

This paper contains 18 sections, 16 equations, 11 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Interpretable polynomial learning for time series
  4. Feature interpretability: dual focus on individual features and feature interactions
  5. Interpretability imperatives in time-series forecasting
  6. Interpretable polynomial learning model
  7. Interpretable polynomial learning algorithm for time series
  8. Simulated data analysis under the squared loss
  9. Importance of temporal dependencies in time series
  10. Advantages of IPL in providing feature interpretability
  11. Perturbation analysis
  12. Bitcoin historical price data analysis under the hinge loss
  13. Importance of temporal dependencies in time series
  14. Advantages of IPL in identifying important features
  15. Field experiment: Antenna health management
  16. ...and 3 more sections

Figures (11)

  • Figure 1: A comparison of different interpretable time-series forecasting methods
  • Figure 2: Importance of time-related target variables ("-x6" denotes a 6-dimensional input formed by combining the original features with one lagged target variable, "-x7" with two lagged target variables, and so on).
  • Figure 3: Top important features identified by different interpretability methods (note: features shown on the horizontal axis that are present in the objective function are highlighted in red; red and blue bars in the chart represent negative and positive values, respectively).
  • Figure 4: Radar charts comparing the performance of interpretability methods (closer proximity to the outer boundary indicates stronger capability in that dimension).
  • Figure 5: Perturbation analysis (the most important feature selected by each method is indicated in parentheses).
  • ...and 6 more figures

Theorems & Definitions (2)

  • Definition 1
  • Remark 1