Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Kolmogorov-Arnold Networks for Time Series Granger Causality Inference

Meiliang Liu, Yunfang Xu, Zijin Li, Zhengye Si, Xiaoxiao Yang, Xinyue Yang, Zhiwen Zhao

TL;DR

An algorithm based on time-reversed Granger causality that automatically selects causal relationships with better inference performance from the original or time-reversed time series or integrates the results to mitigate spurious connectivities is proposed.

Abstract

We propose the Granger causality inference Kolmogorov-Arnold Networks (KANGCI), a novel architecture that extends the recently proposed Kolmogorov-Arnold Networks (KAN) to the domain of causal inference. By extracting base weights from KAN layers and incorporating the sparsity-inducing penalty and ridge regularization, KANGCI effectively infers the Granger causality from time series. Additionally, we propose an algorithm based on time-reversed Granger causality that automatically selects causal relationships with better inference performance from the original or time-reversed time series or integrates the results to mitigate spurious connectivities. Comprehensive experiments conducted on Lorenz-96, Gene regulatory networks, fMRI BOLD signals, VAR, and real-world EEG datasets demonstrate that the proposed model achieves competitive performance to state-of-the-art methods in inferring Granger causality from nonlinear, high-dimensional, and limited-sample time series.

Kolmogorov-Arnold Networks for Time Series Granger Causality Inference

TL;DR

An algorithm based on time-reversed Granger causality that automatically selects causal relationships with better inference performance from the original or time-reversed time series or integrates the results to mitigate spurious connectivities is proposed.

Abstract

We propose the Granger causality inference Kolmogorov-Arnold Networks (KANGCI), a novel architecture that extends the recently proposed Kolmogorov-Arnold Networks (KAN) to the domain of causal inference. By extracting base weights from KAN layers and incorporating the sparsity-inducing penalty and ridge regularization, KANGCI effectively infers the Granger causality from time series. Additionally, we propose an algorithm based on time-reversed Granger causality that automatically selects causal relationships with better inference performance from the original or time-reversed time series or integrates the results to mitigate spurious connectivities. Comprehensive experiments conducted on Lorenz-96, Gene regulatory networks, fMRI BOLD signals, VAR, and real-world EEG datasets demonstrate that the proposed model achieves competitive performance to state-of-the-art methods in inferring Granger causality from nonlinear, high-dimensional, and limited-sample time series.
Paper Structure (23 sections, 1 theorem, 20 equations, 5 figures, 5 tables, 1 algorithm)

This paper contains 23 sections, 1 theorem, 20 equations, 5 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Related Works
  3. Background: Neural network-based Granger causality
  4. Related Works
  5. Component-wise nonlinear autoregressive (NAR)
  6. Time reversed Granger causality
  7. Kolmogorov–Arnold Networks (KAN)
  8. Model Architecture
  9. Component-wise KAN
  10. Applying sparsity-inducing penalty and ridge regularization on KAN to infer Granger causality
  11. Fusion of origin and time reversed time series
  12. Experiment
  13. Lorenz-96
  14. Gene regulatory networks
  15. Dream-3
  16. ...and 8 more sections

Key Result

Theorem 2.1

Let $f:[0,1]^n\to \mathbb{R}$ be a continuous multivariate function. There exist continuous univariate functions $\Phi_q$ and $\phi_{q,p}$ such that: where $\Phi_i:\mathbb{R}\to \mathbb{R}$ and $\phi_{q,p}:[0, 1] \to \mathbb{R}$ are continuous functions.

Figures (5)

  • Figure 1: The architecture of KANGCI.
  • Figure 2: The analysis pipeline of real-world whisker stimulation rat EEG signals. Step 1: EEG electrode positions. A solenoid is used to stimulate the unilateral whisker of the rat, with nodes 1-7 representing the ipsilateral electrodes to stimulation and nodes 9-15 representing the contralateral electrodes to stimulation. Step 2: Extracting the time period to be analyzed. Step 3: Inferring the Granger causality from time series using KANGCI. Step 4: Validating whether the inferred Granger causality matches the physiological response of rats.
  • Figure 3: (a) The inferred Granger causality in epoch -100-0 ms. (b) The Granger causality driving of each channel.
  • Figure 4: (a) The inferred Granger causality in epoch 10-20 ms. (b) The causal driving of each channel.
  • Figure 5: (a) The inferred Granger causality in epoch 20-30 ms. (b) The causal driving of each channel.

Theorems & Definitions (1)

  • Theorem 2.1