Score-based methods for learning Bayesain networks(BN) aim to maximizing the
global score functions. However, if local variables have direct and indirect
dependence simultaneously, the global optimization on score functions misses
edges between variables with indirect dependent relationship, of which scores
are smaller than those with direct dependent relationship. In this paper, we
present an identifiability condition based on a determined subset of parents to
identify the underlying DAG. By the identifiability condition, we develop a
two-phase algorithm namely optimal-tuning (OT) algorithm to locally amend the
global optimization. In the optimal phase, an optimization problem based on
first-order Hilbert-Schmidt independence criterion (HSIC) gives an estimated
skeleton as the initial determined parents subset. In the tuning phase, the
skeleton is locally tuned by deletion, addition and DAG-formalization
strategies using the theoretically proved incremental properties of high-order
HSIC. Numerical experiments for different synthetic datasets and real-world
datasets show that the OT algorithm outperforms existing methods. Especially in
Sigmoid Mix model with the size of the graph being ${\rm\bf d=40}$, the
structure intervention distance (SID) of the OT algorithm is 329.7 smaller than
the one obtained by CAM, which indicates that the graph estimated by the OT
algorithm misses fewer edges compared with CAM.

通过确定一组父节点的可识别性条件，本文提出了一种基于最优调整算法的学习贝叶斯网络的方法，使用 Hilbert-Schmidt 独立性准则进行优化问题，证明了高阶 HSIC 的增量属性，实验证明该算法在不同合成数据集和实际数据集上优于现有方法，在 Sigmoid 混合模型中，算法的结构干预距离（SID）比 CAM 算法小 329.7，表明该算法对图的估计缺少的边更少。