arXiv 论文：用团约束改进精确因果结构学习
Clique Constraints for Exact Causal Structure Learning
做因果发现的朋友可以看看这篇：给精确因果结构学习加了团大小上界约束，实测发现它不是万能加速器，效果看图密度和割管理策略。如果你在用 branch-and-cut 求解器跑结构学习，文中的 Big-M 界收紧和 C3 修复策略能直接借鉴。
一篇 arXiv 论文提出在精确基于评分的因果结构学习中加入无向骨架最大团规模的上界约束，在整数候选点通过惰性循环与团约束强制执行。作者在线性高斯静态 Erdős-Rényi 与无标度 DAG 上系统评估了回调顺序、多种团割平面策略、可行解修复、分数分离和 Big-M 界。其中两个变体受到重点关注：B3 在每次回调中选取违反最严重的最小 (k+1)-团不等式；C3 则通过删除违反约束的边并用基于 QR 的最小二乘重拟合相关回归列来修复不可行整数候选解。
实验结果同时报告因果恢复指标与最优性间隙、原始/对偶界、节点吞吐量、MIPSOL 事件及回调开销。结论显示团约束并不会普遍加速优化，其收益取决于图密度、样本量和割平面管理策略，大量相关约束反而可能降低节点吞吐量。更紧的 Big-M 有效界在多数测试设定下缩小了固定预算下的最优性间隙，但不一定改变固定时限内的 SHD 或 F1。论文还指出选择性分离与可行解修复是后续有前景的方向。
Clique Constraints for Exact Causal Structure Learning
Exact score-based causal structure learning supports explicit structural constraints and optimisation certificates, but its branch-and-cut search can be computationally demanding. We augment exact causal structure learning methods with an upper bound on the maximum clique size of the learned undirected skeleton, enforced at integer candidates through lazy cycle and clique constraints. On static linear-Gaussian Erdős-Rényi and scale-free DAGs, we evaluate callback order, alternative clique-cut policies, incumbent repair, fractional separation, and Big-M bounds. We report causal-recovery metrics jointly with optimality gaps, primal and dual bounds, node throughput, MIPSOL events, and callback cost. Two variants receive particular attention: B3 selects the most violated minimal (k+1)-clique inequality at each callback, whereas C3 repairs an infeasible integer candidate by deleting violating edges and refitting affected regression columns using QR-based least squares. The results do not indicate that clique constraints uniformly accelerate optimisation. However, their benefit depends on graph density, sample size, and cut-management policy, while large collections of correlated constraints can reduce node throughput. Tighter valid Big-M bounds reduced the fixed-budget optimality gap in most tested settings, without necessarily changing SHD or F1 at a fixed time limit. These findings characterize the computational trade-offs of clique-constrained exact causal learning, and identify selective separation and incumbent repair as promising directions.
本条情报归属 AITOP「论文」核心追踪栏目。涉及核心实体与技术议题包括：因果推断、因果结构学习、branch-and-cut、Big-M，读者可通过下方标签进入对应专题页查阅历史脉络与关联对比。
信源核验说明：本文原始线索采编自「arXiv cs.LG」（@Xiaoyu He, Pavel Rytíř, Petr Ryšavý, Jakub Mareček），经 AITOP 多维评分管线结构化提炼。