Directed acyclic graphs are widely used to describe directional pairwise relations. Such relations are estimated by reconstructing a directed acyclic graph's structure, which is challenging when the ordering of nodes of the graph is unknown. In such a situation, existing methods such as the neighbourhood and search-and-score methods have high estimation errors or computational complexities, especially when a local or sequential approach is used to enumerate edge directions by testing or optimizing a criterion locally, as a local method may break down even for moderately sized graphs. We propose a novel approach to simultaneously identifying all estimable directed edges and model parameters, using constrained maximum likelihood with nonconvex constraints. We develop a constraint reduction method that constructs a set of active constraints from super-exponentially many constraints. This, coupled with an alternating direction method of multipliers and a difference convex method, permits efficient computation for large-graph learning. We show that the proposed method consistently reconstructs identifiable directions of the true graph and achieves the optimal performance in terms of parameter estimation. Numerically, the method compares favourably with competitors. A protein network is analysed to demonstrate that the proposed method can make a difference in identifying the network's structure.

中文翻译：

---

重构有向无环高斯图的约束似然

有向无环图被广泛用于描述有向成对关系。这种关系是通过重建有向无环图的结构来估计的，当图的节点顺序未知时，这是具有挑战性的。在这种情况下，现有方法（例如邻域法和搜索评分法）具有很高的估计误差或计算复杂性，尤其是当使用局部或顺序方法通过局部测试或优化准则来枚举边缘方向时，作为局部即使对于中等大小的图，方法也可能会崩溃。我们提出了一种新颖的方法来同时识别所有可估计的有向边和模型参数，使用具有非凸约束的约束最大似然。我们开发了一种约束减少方法，该方法从超指数的许多约束中构造一组主动约束。这与乘法器的交替方向方法和差分凸方法相结合，可以有效地计算大图学习。我们表明，所提出的方法一致地重建了真实图的可识别方向，并在参数估计方面达到了最佳性能。在数值上，该方法与竞争对手相比具有优势。分析蛋白质网络以证明所提出的方法可以在识别网络结构方面有所作为。我们表明，所提出的方法一致地重建了真实图的可识别方向，并在参数估计方面达到了最佳性能。在数值上，该方法与竞争对手相比具有优势。分析蛋白质网络以证明所提出的方法可以在识别网络结构方面有所作为。我们表明，所提出的方法一致地重建了真实图的可识别方向，并在参数估计方面达到了最佳性能。在数值上，该方法与竞争对手相比具有优势。分析蛋白质网络以证明所提出的方法可以在识别网络结构方面有所作为。