TY - JOUR
T1 - Constrained likelihood for reconstructing a directed acyclic Gaussian graph
AU - Yuan, Yiping
AU - Shen, Xiaotong
AU - Pan, Wei
AU - Wang, Zizhuo
N1 - Publisher Copyright:
© 2018 Biometrika Trust.
PY - 2019/3/1
Y1 - 2019/3/1
N2 - 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.
AB - 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.
KW - Acyclicity
KW - Constraint reduction
KW - Directional relation
KW - Nonconvex minimization
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U2 - 10.1093/biomet/asy057
DO - 10.1093/biomet/asy057
M3 - Article
C2 - 30799877
AN - SCOPUS:85063230086
SN - 0006-3444
VL - 106
SP - 109
EP - 125
JO - Biometrika
JF - Biometrika
IS - 1
ER -