Granger Causality Detection with Kolmogorov-Arnold Networks

TL;DR

The paper addresses the challenge of detecting Granger causal relationships in multivariate time series beyond linear dependencies. It introduces GC-KAN, a per-target Kolmogorov-Arnold Network framework that uses spline-based activations and a proximal sparsity step to identify Granger-causal inputs, and compares its performance to the cMLP approach on both VAR-based linear systems and nonlinear Lorenz-96 dynamics. GC-KAN achieves competitive or superior causal-detection accuracy, particularly in high-dimensional or data-limited settings, while producing clearly interpretable causal maps through sparsity in the first-layer mappings. This work demonstrates a scalable, interpretable AI-driven approach to causality discovery in dynamical systems with potential to yield symbolic representations of causal relationships.

Abstract

Discovering causal relationships in time series data is central in many scientific areas, ranging from economics to climate science. Granger causality is a powerful tool for causality detection. However, its original formulation is limited by its linear form and only recently nonlinear machine-learning generalizations have been introduced. This study contributes to the definition of neural Granger causality models by investigating the application of Kolmogorov-Arnold networks (KANs) in Granger causality detection and comparing their capabilities against multilayer perceptrons (MLP). In this work, we develop a framework called Granger Causality KAN (GC-KAN) along with a tailored training approach designed specifically for Granger causality detection. We test this framework on both Vector Autoregressive (VAR) models and chaotic Lorenz-96 systems, analysing the ability of KANs to sparsify input features by identifying Granger causal relationships, providing a concise yet accurate model for Granger causality detection. Our findings show the potential of KANs to outperform MLPs in discerning interpretable Granger causal relationships, particularly for the ability of identifying sparse Granger causality patterns in high-dimensional settings, and more generally, the potential of AI in causality discovery for the dynamical laws in physical systems.

Figures (2)

• Figure 1: Example comparison of Granger causality detection by cMLP with H penalty and GC-KAN against the ground truth. Data is generated from $n = 10$ VAR(3) model. The plots illustrate results from a single cMLP and GC-KAN, focusing on a specific target series. The x-axis represents the input series, while the y-axis corresponds to the input lags. Plots (b) and (c) demonstrate that both cMLP and GC-KAN correctly identify the Granger causal parents of the target series, as indicated by the ground truth in (a). However, the two models differ in their distribution of contributions across different lags, with GC-KAN showing a more even contribution profile compared to cMLP.
• Figure A.1: Two identical KANs were trained using the same sets of training parameters on the same VAR(1) data with 10 variables and input max lag $p=5$ for a specific target series. Network structure from bottom to top of the plots are [50,1,1] representing 50 inputs, 1 hidden neuron and 1 output neuron. Fig.(a) shows the standard training output, Fig.(b) illustrates the result when KAN is trained with proximal operator applied to the input layers. The darkness of the connecting edges represents the strength of the contribution of the inputs to the output, with darker edges indicating stronger contributions.