提出函数型因果影响分析，揭示非线性时间序列中因果关系的动态变化特征。
Function-Valued Causal Influence in Nonlinear Time Series
- 用函数形式替代标量分数，捕捉因果效应随状态变化的动态行为
- 合成实验显示相同得分下因果函数可呈单调、阈值、饱和等多种形态
- 适用于研究政治发展等复杂系统中分阶段、不对称的因果机制
时间序列因果发现越来越多地采用非线性机器学习模型，但结果通常以标量边权分数总结。我们指出，这掩盖了非线性自回归模型实际学习到的核心对象：一种随状态变化的函数，其影响在不同阶段、幅度和情境下差异显著。本文针对可加性、贡献可分解架构，形式化了函数型因果影响，并证明标量因果分数构成严重信息瓶颈，混淆了状态间变异与状态内残差噪声。以神经加性向量自回归（Neural Additive Vector Autoregression）为例，提出基于个体条件期望的实用框架，直接从训练好的模型中估计因果响应函数。通过可控的合成实验，我们证明具有不可区分标量分数的边可能表现出定性不同的函数行为，包括单调、阈值、饱和及符号变化效应。在民主化进程的应用案例中，函数型分析揭示了评分中心方法所遗漏的制度特定与非对称因果结构。
原文摘要 · Abstract (English)
Causal discovery in time series is increasingly performed using nonlinear machine-learning models, yet the resulting causal relationships are almost always summarized by scalar edge scores. We argue that this practice obscures the true object learned by nonlinear autoregressive models: a state-dependent function whose effect varies across regimes, magnitudes, and contexts. We formalize function-valued causal influence for additive, contribution-decomposable architectures and show that scalar causal scores constitute a severe information bottleneck, conflating between-state variation with within-state residual noise. Using Neural Additive Vector Autoregression as a representative architecture, we introduce a practical framework based on Individual Conditional Expectation for estimating causal response functions directly from trained models. Through controlled synthetic experiments, we demonstrate that edges with indistinguishable scalar scores can exhibit qualitatively different functional behaviors, including monotonic, thresholded, saturating, and sign-changing effects. An applied case study on democratic development further shows that function-valued analysis reveals regime-specific and asymmetric causal structure systematically missed by score-centric approaches.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。