Goudie Robert J B, Mukherjee Sach
Medical Research Council Biostatistics Unit Cambridge CB2 0SR, UK.
German Centre for Neurodegenerative Diseases (DZNE) Bonn 53175, Germany.
J Mach Learn Res. 2016 Apr;17(30):1-39.
We propose a Gibbs sampler for structure learning in directed acyclic graph (DAG) models. The standard Markov chain Monte Carlo algorithms used for learning DAGs are random-walk Metropolis-Hastings samplers. These samplers are guaranteed to converge asymptotically but often mix slowly when exploring the large graph spaces that arise in structure learning. In each step, the sampler we propose draws entire sets of parents for multiple nodes from the appropriate conditional distribution. This provides an efficient way to make large moves in graph space, permitting faster mixing whilst retaining asymptotic guarantees of convergence. The conditional distribution is related to variable selection with candidate parents playing the role of covariates or inputs. We empirically examine the performance of the sampler using several simulated and real data examples. The proposed method gives robust results in diverse settings, outperforming several existing Bayesian and frequentist methods. In addition, our empirical results shed some light on the relative merits of Bayesian and constraint-based methods for structure learning.
我们提出了一种用于有向无环图（DAG）模型结构学习的吉布斯采样器。用于学习DAG的标准马尔可夫链蒙特卡罗算法是随机游走梅特罗波利斯-黑斯廷斯采样器。这些采样器保证能渐近收敛，但在探索结构学习中出现的大型图空间时，通常混合速度较慢。在每一步中，我们提出的采样器从适当的条件分布中为多个节点抽取整个父节点集。这提供了一种在图空间中进行大步移动的有效方法，允许更快地混合，同时保留收敛的渐近保证。条件分布与变量选择有关，候选父节点起着协变量或输入的作用。我们使用几个模拟和真实数据示例对采样器的性能进行了实证检验。所提出的方法在不同设置下都能给出稳健的结果，优于几种现有的贝叶斯和频率主义方法。此外，我们的实证结果揭示了贝叶斯方法和基于约束的方法在结构学习方面的相对优点。
