发表机构
Seoul National University（首尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出FiCS算法，利用局部Fisher信息在加性噪声模型中进行稀疏因果发现，通过Fisher父节点补全实现排序与父节点选择，并在理论上证明高维一致性，实验验证了其有效性。
AI 中文摘要
稀疏因果发现需要利用图结构而无需估计高维密度的方法。我们提出了Fisher信息补全搜索（FiCS），一种针对加性噪声模型的源优先算法，该算法使用一个局部Fisher得分同时进行排序和父节点选择。在正则性和非恒定父节点条件下，我们证明当条件集包含所有父节点且不包含后代时，节点的局部Fisher信息恰好等于噪声Fisher信息。这种Fisher父节点补全将父节点集识别为唯一的最小Fisher补全。当最大条件集大小$q$至少为最大入度$d$时，总体FiCS查询至多$q+1$个变量的边缘分布，并在正排序裕度下恢复真实的DAG。有界条件化也具有总体优势：将$q$减小至$d$不会降低排序裕度，且可能严格增加排序裕度。一个增长的非高斯族将局部Fisher选择与条件方差和叶优先Fisher排序区分开来。对于正则化核Stein估计器，我们在$q\{1+\log(p/q)\}+\log p=o(n)$、均匀Fisher分离、局部近似以及兼容的岭和父节点惩罚参数下建立了高维DAG一致性。实验表明，当$n$相对于$p$较小时增益最强，量化了条件化大小的影响，并在三个真实数据基准上展示了具有竞争力的参考图恢复。
英文摘要
Sparse causal discovery calls for methods that exploit graph structure without estimating high-dimensional densities. We introduce Fisher Information Completion Search (FiCS), a source-first algorithm for additive noise models that uses one local Fisher score for both ordering and parent selection. Under regularity and nonconstant-parent conditions, we prove that a node's local Fisher information equals the noise Fisher information exactly when the conditioning set contains all parents, provided that it contains no descendants. This Fisher parent completion identifies the parent set as the unique minimal Fisher completion. With a maximum conditioning set size $q$ at least the maximum indegree $d$, population FiCS queries marginals of at most $q+1$ variables and recovers the true directed acyclic graph under a positive ordering margin. Bounded conditioning also has a population advantage: reducing $q$ toward $d$ cannot decrease, and can strictly increase, the ordering margin. A growing non-Gaussian family separates local Fisher selection from conditional-variance and leaf-first Fisher ordering. For the regularized kernel Stein estimator, we establish high-dimensional DAG consistency under $q\{1+\log(p/q)\}+\log p=o(n)$, uniform Fisher separation, local approximation, and compatible ridge and parent penalty parameters. Experiments show the strongest gains when $n$ is small relative to $p$, quantify the effect of the conditioning size, and demonstrate competitive reference-graph recovery on three real-data benchmarks.
