Bayesian DAG Structure Learning with Simultaneous Shrinkage Covariance Estimation under Scale-Mixture Error Distributions in the Proportional High-Dimensional Regime
比例高维下尺度混合误差的贝叶斯DAG结构学习与收缩协方差估计
We propose a unified Bayesian framework namely robust DAG-Cholesky horseshoe (R-DACH) for joint directed acyclic graph (DAG) structure learning and precision matrix estimation in the high-dimensional proportional asymptotic regime $p/n \to c \in (0,\infty)$, under the scale mixture of normal errors. The construction places a global-local horseshoe-type prior directly on the strictly lower-triangular entries of the modified Cholesky factor of the DAG-Markov precision matrix,…