带反馈的因果发现中的统计代价

中文摘要 AI 辅助

什么决定了学习循环因果结构的不可避免的样本代价？对于循环线性非高斯模型，我们研究从观测数据中进行精确凝聚恢复：识别强连通分量（SCC）划分以及分量之间的所有边。我们为这一目标建立了首个关于样本复杂度的信息论下界。对于 $p$ 个变量、最大SCC大小 $s_{\max}$ 和最大外部父节点数 $d_B$，在正则模型类的最坏情况下，任何估计器都需要 $s_{\max}\log(ep/s_{\max})+d_B\log(ep/d_B)$ 量级的样本。这些界区分了SCC成员资格和外部父节点选择的代价。在主可逆性和无相关性忠实性条件下，我们建立了一个总体块外生性原则，通过残差独立性和包含最小性来识别未知的根SCC。一个稀疏调整特征表明，小的调整集足以识别SCC及其直接外部父节点，而无需对所有先前恢复的变量进行回归。这些特征产生了BlockExo算法，在适当条件下，该算法在不知道 $s_{\max}$ 或 $d_B$ 的情况下达到了结构匹配的样本界。模拟实验支持我们样本界的结构依赖性，并展示了BlockExo在与其他循环因果发现方法比较中的样本高效恢复能力。

英文摘要

What determines the unavoidable sample cost of learning cyclic causal structure? For cyclic linear non-Gaussian models, we study exact condensation recovery from observational data: identifying the strongly connected component (SCC) partition and all edges between components. We establish the first information-theoretic lower bounds on sample complexity for this target. For $p$ variables, maximum SCC size $s_{\max}$, and maximum external-parent count $d_B$, any estimator requires order $s_{\max}\log(ep/s_{\max})+d_B\log(ep/d_B)$ samples in the worst case over a regular model class. These bounds distinguish the costs of SCC membership and external-parent selection. Under principal invertibility and without correlation faithfulness, we establish a population block-exogeneity principle that identifies unknown root SCCs through residual independence and inclusion minimality. A sparse-adjustment characterization shows that small adjustment sets suffice to identify SCCs and their direct external parents, without regressing on all previously recovered variables. These characterizations yield BlockExo, which attains a structurally matching sample bound without knowing $s_{\max}$ or $d_B$ under suitable conditions. Simulations support the structural dependence of our sample bound and demonstrate BlockExo's sample-efficient recovery in comparisons with other methods for cyclic causal discovery.

发表机构

• Seoul National University（首尔国立大学）
• Princeton University（普林斯顿大学）

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