Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Unmixing Noise from Hawkes Process to Model Learned Physiological Events

Guillaume Staerman, Virginie Loison, Thomas Moreau

TL;DR

This work introduces UNHaP (Unmix Noise from Hawkes Processes), a novel approach addressing the joint learning of temporal structures in events and the removal of spurious detections.

Abstract

Physiological signal analysis often involves identifying events crucial to understanding biological dynamics. Traditional methods rely on handcrafted procedures or supervised learning, presenting challenges such as expert dependence, lack of robustness, and the need for extensive labeled data. Data-driven methods like Convolutional Dictionary Learning (CDL) offer an alternative but tend to produce spurious detections. This work introduces UNHaP (Unmix Noise from Hawkes Processes), a novel approach addressing the joint learning of temporal structures in events and the removal of spurious detections. Leveraging marked Hawkes processes, UNHaP distinguishes between events of interest and spurious ones. By treating the event detection output as a mixture of structured and unstructured events, UNHaP efficiently unmixes these processes and estimates their parameters. This approach significantly enhances the understanding of event distributions while minimizing false detection rates.

Unmixing Noise from Hawkes Process to Model Learned Physiological Events

TL;DR

This work introduces UNHaP (Unmix Noise from Hawkes Processes), a novel approach addressing the joint learning of temporal structures in events and the removal of spurious detections.

Abstract

Physiological signal analysis often involves identifying events crucial to understanding biological dynamics. Traditional methods rely on handcrafted procedures or supervised learning, presenting challenges such as expert dependence, lack of robustness, and the need for extensive labeled data. Data-driven methods like Convolutional Dictionary Learning (CDL) offer an alternative but tend to produce spurious detections. This work introduces UNHaP (Unmix Noise from Hawkes Processes), a novel approach addressing the joint learning of temporal structures in events and the removal of spurious detections. Leveraging marked Hawkes processes, UNHaP distinguishes between events of interest and spurious ones. By treating the event detection output as a mixture of structured and unstructured events, UNHaP efficiently unmixes these processes and estimates their parameters. This approach significantly enhances the understanding of event distributions while minimizing false detection rates.
Paper Structure (24 sections, 27 equations, 7 figures, 5 tables, 1 algorithm)

This paper contains 24 sections, 27 equations, 7 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background on Marked Hawkes Processes
  3. Unmixing Noise from Hawkes Process
  4. Numerical Validation
  5. Joint inference and unmixing with UNHaP
  6. Benchmarking inference and computation time
  7. Application to Physiological Data
  8. Discussion
  9. Technical Details
  10. Detailing UNHaP loss with discretization
  11. Initialization with Moments Matching
  12. Gradients of the UNHaP loss
  13. Additional Experiments
  14. Sensitivity analysis of the alternate minimization parameter
  15. Further experiments on the recovery of the mixture structure
  16. ...and 9 more sections

Figures (7)

  • Figure 1: Illustration of the UNHaP framework. The goal of UNHaP is to distinguish between structured events ( green) and spurious ones ( red) by identifying the structure of the MMHP ( grey) from the observed events ( blue).
  • Figure 2: Parameters estimation errors for UNHaP and "jointfadin" for varying $T$ w.r.t. different values of $\tilde{\mu}$ with linear (left) and uniform (right) distributions on noisy marks.
  • Figure 3: Precision/Recall values for the estimation of $\rho$ for different values of $T$ w.r.t. $\alpha$ with linear (left) and uniform (right) distributions on noisy marks.
  • Figure 4: Experimental pipeline on ECG Data. (A) Sub-sample of raw ECG plot. (B) Output of Convolutional Dictionary Learning algorithm: (B1) learned temporal atom representing one heartbeat, (B2) detected events on the time interval. (C) Output of UNHaP: (C1) Estimated Hawkes parameters: noise baseline (red), baseline (pink), and kernel (grey). The kernel is very close to the ground truth (orange dashed). (C2) Unmixing output $\rho$: events were classified either belonging to the Hawkes Process ( green) or as spurious noisy events ( red).
  • Figure B.1: Inference comparison regarding the batch size of Hawkes parameters gradients between each $\rho$ update. The error estimation on Hawkes parameters (left), the Precision score on the $\rho$ recovering (middle) and the associated computational time (right) are displayed for non-noisy (top) and noisy settings (bottom).
  • ...and 2 more figures