精确构建：线性有向无环图的由底向上推断
BUILD with Precision: Bottom-Up Inference of Linear DAGs
AI总结：
提出BUILD算法，利用等噪声方差线性高斯SEM下观测数据的集成精度矩阵的独特结构，通过确定性逐步方法精确重构DAG，并在有限数据下通过周期性重估计精度矩阵增强鲁棒性。
摘要：
从观测数据中学习有向无环图（DAG）的结构是因果发现、统计信号处理和机器学习中的核心问题。在等噪声方差的线性高斯结构方程模型（SEM）下，该问题是可识别的，并且我们证明观测数据的集成精度矩阵展现出一种有助于DAG恢复的独特结构。利用这一性质，我们提出了BUILD（线性DAG的由底向上推断），一种确定性的逐步算法，该算法识别叶节点及其父节点，然后通过移除关联边来修剪叶节点以进入下一步，从真实的精度矩阵中精确重构DAG。在实践中，精度矩阵必须从有限数据中估计，而病态条件可能导致BUILD步骤中的误差累积。作为一种缓解策略，我们定期重新估计精度矩阵（随着叶节点被修剪，变量减少），以运行时换取增强的鲁棒性。在具有挑战性的合成基准上的可重复结果表明，BUILD与最先进的DAG学习算法相比具有优势，同时提供了对复杂性的明确控制。
英文摘要：
Learning the structure of directed acyclic graphs (DAGs) from observational data is a central problem in causal discovery, statistical signal processing, and machine learning. Under a linear Gaussian structural equation model (SEM) with equal noise variances, the problem is identifiable and we show that the ensemble precision matrix of the observations exhibits a distinctive structure that facilitates DAG recovery. Exploiting this property, we propose BUILD (Bottom-Up Inference of Linear DAGs), a deterministic stepwise algorithm that identifies leaf nodes and their parents, then prunes the leaves by removing incident edges to proceed to the next step, exactly reconstructing the DAG from the true precision matrix. In practice, precision matrices must be estimated from finite data, and ill-conditioning may lead to error accumulation across BUILD steps. As a mitigation strategy, we periodically re-estimate the precision matrix (with less variables as leaves are pruned), trading off runtime for enhanced robustness. Reproducible results on challenging synthetic benchmarks demonstrate that BUILD compares favorably to state-of-the-art DAG learning algorithms, while offering an explicit handle on complexity.
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