Learning graphical conditional independence structures is an important
machine learning problem and a cornerstone of causal discovery. However, the
accuracy and execution time of learning algorithms generally struggle to scale
to problems with hundreds of highly connected variables -- for instance,
recovering brain networks from fMRI data. We introduce the best order score
search (BOSS) and grow-shrink trees (GSTs) for learning directed acyclic graphs
(DAGs) in this paradigm. BOSS greedily searches over permutations of variables,
using GSTs to construct and score DAGs from permutations. GSTs efficiently
cache scores to eliminate redundant calculations. BOSS achieves
state-of-the-art performance in accuracy and execution time, comparing
favorably to a variety of combinatorial and gradient-based learning algorithms
under a broad range of conditions. To demonstrate its practicality, we apply
BOSS to two sets of resting-state fMRI data: simulated data with
pseudo-empirical noise distributions derived from randomized empirical fMRI
cortical signals and clinical data from 3T fMRI scans processed into cortical
parcels. BOSS is available for use within the TETRAD project which includes
Python and R wrappers.

通过引入最佳次序得分搜索（BOSS）和增长 - 收缩树（GSTs）方法，我们在学习因果图过程中提出了一种有效的方法，其能够解决包含数百个高度连接变量的问题，例如从 fMRI 数据中恢复脑网络。通过在变量的排列组合上进行贪婪搜索，并使用 GSTs 来构建和评分有向无环图，BOSS 具有最先进的准确性和执行时间，可以在广泛的条件下与各种组合和基于梯度的学习算法相比较。我们还将 BOSS 应用于两组静息态 fMRI 数据，包括从随机经验 fMRI 皮层信号导出的伪经验噪声分布的模拟数据和处理成皮层分区的 3T fMRI 扫描的临床数据，结果证明了 BOSS 的实用性。BOSS 可在包括 Python 和 R 封装的 TETRAD 项目中使用。