arXiv:2605.21846stat.MEcs.LG2026-05

在噪声方差相等假设下,发现时间序列中的因果关系。

Causal Discovery in Structural VAR Models Under Equal Noise Variance

论文配图:Causal Discovery in Structural VAR Models Under Equal Noise Variance
图 1 · 摘自论文原文
  • 基于噪声方差相等的线性高斯结构VAR模型,提出新因果发现方法。
  • 多个参数化可产生相同观测过程,需在等价类中寻找稀疏解。
  • 适用于神经科学等采样较慢但存在同期效应的场景。

多变量时间序列的因果发现面临挑战,因为因果效应可能既跨时间又发生在同一采样间隔内。这一问题在神经科学中尤为关键,因采样率常低于底层动态变化,且同期效应未必构成无环图。本文研究在线性高斯结构向量自回归(structural VAR)模型下,当结构噪声项具有相同方差时的因果发现。不同于传统的无向图(DAG)横截面等噪声方差设定,该时间序列设定通常无法唯一确定因果图。多个结构VAR参数化可诱导相同的平稳观测过程分布。本文引入一种针对此设定的观测等价性概念,并证明其等价类由结构方程的正交变换及全局正尺度缩放所刻画。由此导出一种等价感知的模型差异度量——观测对齐差异,用于比较在保持观测律不变的变换下的结构模型。基于此理论,提出ENVAR方法:在诱导的观测等价类中搜索一个稀疏归一化的结构代表。在合成结构VAR数据和一项fMRI数据集上评估了该方法。

原文摘要 · Abstract (English)

Causal discovery from multivariate time series is challenging when causal effects may occur both across time and within the same sampling interval. This issue is especially important in applications such as neuroscience, where the sampling rate may be coarse relative to the underlying dynamics and contemporaneous effects need not form an acyclic graph. We study causal discovery in linear Gaussian structural VAR models under an equal noise variance assumption, meaning that the structural noise terms have a common variance. Unlike the DAG-based cross-sectional equal noise variance setting, the time-series setting considered here does not generally yield point identification of a unique causal graph. Instead, multiple structural VAR parameterizations can induce the same stationary observed process law. We introduce a notion of observational equivalence tailored to this setting and show that the corresponding equivalence class is characterized by orthogonal transformations of the structural equations together with a global positive scale. This characterization leads to an equivalence-aware model discrepancy, the observational alignment discrepancy, which compares structural models modulo transformations that preserve the observed law. Building on this theory, we propose ENVAR, a sparsity-based procedure that searches over the induced observational equivalence class for a sparse normalized structural representative. We evaluate the proposed methodology on synthetic structural VAR data and on an fMRI dataset.

因果发现时间序列VAR模型神经科学

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