Constraint- and Score-Based Nonlinear Granger Causality Discovery with Kernels

2026-01-14

AI Summary

This work addresses the challenge of identifying causal relationships in nonlinear time series, particularly the limitations of existing methods in theoretical coherence and contemporaneous causal discovery. The authors propose a unified framework based on Kernel Principal Component Regression (KPCR), which for the first time integrates two advanced kernel-based Granger causality approaches. By incorporating a scoring model grounded in Gaussian processes and a penalty term derived from the Smoothed Information Criterion (SIC), the method significantly enhances performance in detecting nonlinear causal dependencies. Furthermore, the study introduces the first fully Granger-causality–principled algorithm for contemporaneous causal inference. Experimental results demonstrate that the proposed approach outperforms state-of-the-art methods in nonlinear causal discovery and remains competitive in contemporaneous causal inference tasks.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Kernel-based methods are used in the context of Granger Causality to enable the identification of nonlinear causal relationships between time series variables. In this paper, we show that two state of the art kernel-based Granger Causality (GC) approaches can be theoretically unified under the framework of Kernel Principal Component Regression (KPCR), and introduce a method based on this unification, demonstrating that this approach can improve causal identification. Additionally, we introduce a Gaussian Process score-based model with Smooth Information Criterion penalisation on the marginal likelihood, and demonstrate improved performance over existing state of the art time-series nonlinear causal discovery methods. Furthermore, we propose a contemporaneous causal identification algorithm, fully based on GC, using the proposed score-based $GP_{SIC}$ method, and compare its performance to a state of the art contemporaneous time series causal discovery algorithm.

Problem

• Granger Causality
• nonlinear causal discovery
• time series
• contemporaneous causality
• kernel methods

Innovation

• Kernel-based Granger Causality
• Kernel Principal Component Regression
• Gaussian Process
• Smooth Information Criterion
• Contemporaneous Causal Discovery