Constrained likelihood for reconstructing a directed acyclic Gaussian graph.
Constrained likelihood for reconstructing a directed acyclic Gaussian graph.
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DOI：
10.1093/biomet/asy057
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发表时间：
2018-12
期刊：
影响因子：
2.7
通讯作者：
Yiping Yuan;Xiaotong Shen;W. Pan;Zizhuo Wang
中科院分区：
文献类型：
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作者：
Yiping Yuan;Xiaotong Shen;W. Pan;Zizhuo Wang
有向无环图被广泛用于描述有向对关系。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，这是一个挑战。在这种情况下，现有的方法，如邻域和搜索得分方法，具有很高的估计误差或计算复杂性，特别是当使用局部或顺序方法通过局部测试或优化标准来枚举边缘方向时，因为局部方法即使对于中等大小的图也可能崩溃。我们提出了一种新的方法来同时识别所有可估计的有向边和模型参数，使用约束极大似然与非凸约束。本文提出了一种约束约简方法，将超指数多约束构造为一组活动约束。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。结果表明，该方法能够一致地重建真图的可识别方向，并在参数估计方面达到了最佳性能。在数值上，该方法优于竞争对手。对一个蛋白质网络进行了分析，证明了所提出的方法可以在识别网络结构方面发挥作用。
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.