We propose an approach termed ``qDAGx'' for Bayesian covariate-dependent quantile directed acyclic graphs (DAGs) where these DAGs are individualized, in the sense that they depend on individual-specific covariates. The individualized DAG structure of the proposed approach can be uniquely identified at any given quantile, based on purely observational data without strong assumptions such as a known topological ordering. To scale the proposed method to a large number of variables and covariates, we propose for the model parameters a novel parameter expanded horseshoe prior that affords a number of attractive theoretical and computational benefits to our approach. By modeling the conditional quantiles, qDAGx overcomes the common limitations of mean regression for DAGs, which can be sensitive to the choice of likelihood, e.g., an assumption of multivariate normality, as well as to the choice of priors. We demonstrate the performance of qDAGx through extensive numerical simulations and via an application in precision medicine, which infers patient-specific protein--protein interaction networks in lung cancer.

翻译：我们提出一种名为“qDAGx”的方法，用于构建贝叶斯协变量依赖的分位有向无环图，其中这些有向无环图是个体化的，即它们依赖于个体特定的协变量。该方法中个体化的有向无环图结构可以在任意给定分位数下唯一识别，仅基于纯观测数据，无需强假设（如已知的拓扑排序）。为了将该方法扩展到大量变量和协变量，我们为模型参数提出了一种新颖的参数扩展马蹄形先验，该先验为我们的方法提供了多种有吸引力的理论和计算优势。通过建模条件分位数，qDAGx克服了有向无环图中均值回归的常见局限性，后者可能对似然选择（例如多元正态性假设）以及先验选择敏感。我们通过广泛的数值模拟和精准医学应用（推断肺癌中患者特异性蛋白质-蛋白质相互作用网络）展示了qDAGx的性能。