Kolmogorov-Arnold Networks for Time Series Granger Causality Inference

2025-01-15

AI Summary

Causal discovery in nonlinear, high-dimensional, small-sample time series—such as those arising from the Lorenz-96 system, gene regulatory networks, fMRI, and economic data—remains challenging due to complex nonlinear dependencies and limited observations. Method: This paper proposes a novel Granger causality inference framework based on Kolmogorov–Arnold Networks (KANs). It is the first to integrate KANs into causal modeling, enabling learnable nonlinear basis functions and automatic selection of dynamic time lags. We introduce a temporal reversal contrastive loss, jointly incorporating sparsity-inducing and ridge regularization to suppress spurious connections and enhance robustness in causal direction identification. Results: The method achieves state-of-the-art performance across diverse benchmarks—including Lorenz-96, DREAM, fMRI, and synthetic VAR systems—particularly excelling in low-sample regimes, where it significantly improves accuracy in detecting nonlinear causal relationships.

Technology Category

Machine Learning: Causal LearningReasoning under Uncertainty: CausalityCognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingWeb Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We introduce Granger Causality Kolmogorov-Arnold Networks (GCKAN), an innovative 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 along with ridge regularization, GCKAN infers the Granger causality from time series while enabling automatic time lag selection. Additionally, we propose an algorithm leveraging time-reversed Granger causality to enhance inference accuracy. The algorithm compares prediction and sparse-inducing losses derived from the original and time-reversed series, automatically selecting the casual relationship with the higher score or integrating the results to mitigate spurious connectivities. Comprehensive experiments conducted on Lorenz-96, gene regulatory networks, fMRI BOLD signals, and VAR 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.

Problem

• Causal inference
• Time series analysis
• Complex systems

Innovation

• GCKAN Network
• Time-reversed Causality Algorithm
• Complex Time Series Analysis