统一核方法与高斯过程，提升非线性因果发现准确率
Constraint- and Score-Based Nonlinear Granger Causality Discovery with Kernels
- 基于核主成分回归统一两类先进核方法
- 新模型在多个数据集上优于现有最先进方法
- 无需额外假设，适合时序因果分析研究者
核方法被用于格兰杰因果关系中以识别时间序列变量间的非线性因果关系。本文表明，两种最先进的核格兰杰因果（GC）方法可在核主成分回归（KPCR）框架下理论统一，并提出基于该统一的新方法，证明其可提升因果识别性能。此外，引入一种基于高斯过程的评分模型，采用平滑信息准则（SIC）对边缘似然进行惩罚，实验显示其性能优于现有最先进的时间序列非线性因果发现方法。同时，提出一种完全基于格兰杰因果的同期因果识别算法，利用所提出的GP_{SIC}方法，并与当前最先进的同期时间序列因果发现算法进行对比。
原文摘要 · Abstract (English)
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.
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