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

TL;DR

This paper unifies kernel-based nonlinear Granger causality methods under KPCR, introduces a Gaussian Process score-based model with SIC penalization, and proposes a new algorithm for contemporaneous causal discovery, showing improved performance.

Contribution

It provides a theoretical unification of kernel-based GC methods, introduces a novel GP score-based model with SIC, and develops a new causal discovery algorithm with superior results.

Findings

Unified kernel-based GC approaches under KPCR framework.

Proposed GP score-based model with SIC improves causal detection.

New contemporaneous causal discovery algorithm outperforms existing methods.

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.