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Event Detection in Time Series: Universal Deep Learning Approach

Menouar Azib, Benjamin Renard, Philippe Garnier, Vincent Génot, Nicolas André

TL;DR

This work proposes a novel supervised regression-based deep learning approach that can effectively handle various types of events within a unified framework, including rare events and imbalanced datasets, and demonstrates its superior performance across diverse domains, particularly for rare events and imbalanced datasets.

Abstract

Event detection in time series is a challenging task due to the prevalence of imbalanced datasets, rare events, and time interval-defined events. Traditional supervised deep learning methods primarily employ binary classification, where each time step is assigned a binary label indicating the presence or absence of an event. However, these methods struggle to handle these specific scenarios effectively. To address these limitations, we propose a novel supervised regression-based deep learning approach that offers several advantages over classification-based methods. Our approach, with a limited number of parameters, can effectively handle various types of events within a unified framework, including rare events and imbalanced datasets. We provide theoretical justifications for its universality and precision and demonstrate its superior performance across diverse domains, particularly for rare events and imbalanced datasets.

Event Detection in Time Series: Universal Deep Learning Approach

TL;DR

This work proposes a novel supervised regression-based deep learning approach that can effectively handle various types of events within a unified framework, including rare events and imbalanced datasets, and demonstrates its superior performance across diverse domains, particularly for rare events and imbalanced datasets.

Abstract

Event detection in time series is a challenging task due to the prevalence of imbalanced datasets, rare events, and time interval-defined events. Traditional supervised deep learning methods primarily employ binary classification, where each time step is assigned a binary label indicating the presence or absence of an event. However, these methods struggle to handle these specific scenarios effectively. To address these limitations, we propose a novel supervised regression-based deep learning approach that offers several advantages over classification-based methods. Our approach, with a limited number of parameters, can effectively handle various types of events within a unified framework, including rare events and imbalanced datasets. We provide theoretical justifications for its universality and precision and demonstrate its superior performance across diverse domains, particularly for rare events and imbalanced datasets.
Paper Structure (17 sections, 1 theorem, 34 equations, 8 figures, 2 tables)

This paper contains 17 sections, 1 theorem, 34 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Mathematical Formulation
  3. Overlapping Partitions
  4. Overlapping Parameter Function
  5. Principle of Event Detection
  6. Practical Considerations and Implementations
  7. Numerical Study
  8. Fraud Detection
  9. Setup
  10. Comparison with and without Data Balancing (SMOTE)
  11. Bow Shock Crossings Detection
  12. Setup
  13. Performance Evaluation and Comparative Analysis
  14. Conclusion
  15. Proofs
  16. ...and 2 more sections

Key Result

Theorem 3.1

If $T$ and $T^{-1}$ are continuous, then there exists a feed-forward neural network $f \in \Sigma^{r}(\Psi)$ that utilizes a squashing function $\Psi$. This network can approximate the function $\pi$ from $\mathcal{V}$ to $[0,1]$ with arbitrary precision, given a sufficient number of hidden units $Q where $x \in \mathbb{R}^{r}$, $\beta_j \in \mathbb{R}$, and $A_j \in \mathbf{A}^{r}$. The function

Figures (8)

  • Figure 1: Plot of $op(p_i, e)$ as a function of $t_i + w_s/2$, the middle time of partition $p_i$.
  • Figure 2: The training loss and validation loss of the FFN trained (FFN_0) on the frauds detection case.
  • Figure 3: Comparison between predicted and ground truth $op$ values on the frauds detection case.
  • Figure 4: The training loss and validation loss of the FFN trained (FFN_0) on the bow shock crossings case.
  • Figure 5: Comparison between predicted and ground truth $op$ values on the bow shock crossings case.
  • ...and 3 more figures

Theorems & Definitions (9)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Theorem 3.1
  • proof
  • Definition 1.1
  • Definition 1.2
  • Definition 1.3