Cause-effect inference through spectral independence in linear dynamical systems: theoretical foundations
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线性动态系统中谱独立性因果推断的理论基础
- 研究问题
- 如何用观测时间序列区分因果方向，谱独立性准则具有何种信息论解释、可识别性基础及对降采样的稳健性？
- 方法与思路
- 作者基于因果机制独立原则，研究原因功率谱与生成结果的滤波器频率响应模平方不相关这一准则，并从不变性角度分析。
- 材料陈述的贡献
- 摘要称给出谱独立性的信息论解释、可识别性结果和降采样稳健性分析，并讨论该假设的局限及可能推广。
- 阅读关注点
- 应核对线性滤波系统的具体条件、可识别性覆盖的情形、降采样稳健性的范围，以及谱独立性假设在应用中如何判断。
- 阅读边界
- 这是 arXiv 预印本，同行评审或接收未核实。摘要未列出定理条件，不能据此认定该准则普遍有效或全面优于 Granger 方法。
原文摘要
Distinguishing between cause and effect using time series observational data is a major challenge in many scientific fields. A new perspective has been provided based on the principle of Independence of Causal Mechanisms (ICM), leading to the Spectral Independence Criterion (SIC), postulating that the power spectral density (PSD) of the cause time series is uncorrelated with the squared modulus of the frequency response of the filter generating the effect. Since SIC rests on methods and assumptions in stark contrast with most causal discovery methods for time series, it raises questions regarding what theoretical grounds justify its use. In this paper, we provide answers covering several key aspects. After providing an information theoretic interpretation of SIC, we present an identifiability result that sheds light on the context for which this approach is expected to perform well. We further demonstrate the robustness of SIC to downsampling - an obstacle that can spoil Granger-based inference. Finally, an invariance perspective allows to explore the limitations of the spectral independence assumption and how to generalize it. Overall, these results support the postulate of Spectral Independence is a well grounded leading principle for causal inference based on empirical time series.