通过拉普拉斯近似进行有向无环图的可扩展贝叶斯结构学习及其在乳腺癌基因表达网络中的应用
Scalable Bayesian structure learning of directed acyclic graphs via Laplace approximation, with an application to breast cancer gene expression networks
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中文总结 AI 辅助
研究从观测数据学习有向无环图结构的问题，基于拉普拉斯近似为非共轭正态-伽马先验开发贝叶斯评分函数，嵌入采样器并与临床结果耦合，在模拟和真实数据集上表现良好，能恢复结构并预测肿瘤。
中文摘要 AI 辅助
从观测数据中学习有向无环图（DAG）的结构是因果发现的基础任务，广泛用于从医学和基因组测量中推断调控网络。贝叶斯公式虽能量化模型不确定性并纳入先验生物学知识，但DAG空间的超指数增长及灵活非共轭先验下节点边缘似然的难处理性阻碍了其实际应用。现有闭式解大多限于共轭正态-逆伽马先验。我们为精度矩阵的修正Cholesky参数化上的非共轭正态-伽马先验开发了拉普拉斯近似贝叶斯评分函数，将其嵌入DAG上的Metropolis-Hastings采样器，并通过probit链接将潜在高斯网络与二元临床结果耦合。我们表明节点边缘积分具有广义逆高斯形式，其精确值是第二类修正贝塞尔函数，所提出的评分函数是其大参数渐近形式；每个条件方差的后验同样是广义逆高斯且可精确采样。在模拟中，所提出的先验在临床队列典型样本量下优于共轭基线以及PC、贪婪等价搜索、NOTEARS和DAGMA基准。在两个真实数据集上，该方法恢复了已知结构，并通过DAG-probit扩展，使用一组稀疏、可解释的直接预测因子，以交叉验证的ROC-AUC为0.94从核形态计量学预测恶性肿瘤。
英文摘要
Structure learning of directed acyclic graphs (DAGs) from observational data is a foundational task in causal discovery and is widely used to infer regulatory networks from medical and genomic measurements. The Bayesian formulation quantifies model uncertainty and admits prior biological knowledge, but its practical use has been hampered by the super-exponential growth of the DAG space and by the intractability of the node-marginal likelihood under flexible, non-conjugate priors. Existing closed-form solutions are largely confined to the conjugate Normal--Inverse-Gamma prior. We develop a Laplace-approximated Bayesian scoring function for the non-conjugate Normal--Gamma prior on the modified Cholesky parameterisation of the precision matrix, embed it in a Metropolis--Hastings sampler over DAGs, and couple the latent Gaussian network to a binary clinical outcome through a probit link. We show that the node-marginal integral is of generalised inverse-Gaussian form, so that its exact value is a modified Bessel function of the second kind and the proposed scoring function is its leading large-argument asymptotic; the posterior of each conditional variance is likewise generalised inverse-Gaussian and is sampled exactly. In simulation, the proposed prior improves on the conjugate baseline and on the PC, greedy-equivalence-search, NOTEARS, and DAGMA benchmarks at sample sizes typical of clinical cohorts. On two real datasets, the Sachs protein-signalling network, scored against its validated consensus graph, and the Wisconsin Diagnostic Breast Cancer data, the method recovers known structure and, through the DAG-probit extension, predicts malignancy from nuclear morphometry with a cross-validated ROC-AUC of $0.94$ using a sparse, interpretable set of direct predictors.
