Scalable Bayesian structure learning of directed acyclic graphs via Laplace approximation, with an application to breast cancer gene expression networks
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通过拉普拉斯近似实现可扩展的贝叶斯有向无环图结构学习及乳腺癌应用
- 研究问题
- 在非共轭先验下，如何计算有向无环图的贝叶斯结构评分、表征模型不确定性，并将潜在高斯网络联系到二元临床结果？
- 方法与思路
- 作者对修正 Cholesky 参数化下的非共轭先验构造拉普拉斯评分，配合图空间抽样，并通过 probit 链接连接临床结果。
- 材料陈述的贡献
- 摘要称，节点积分与条件方差具有可解析的分布形式；模拟和两个应用显示结构恢复及预测表现，但这些比较仍需核对。
- 阅读关注点
- 应核对拉普拉斯评分的近似误差、图空间抽样混合、比较基准公平性，以及题名基因表达与摘要核形态测量应用的对应关系。
- 阅读边界
- 这是预印本，不能据此认定已同行评审或期刊接收。摘要未说明因果解释所需条件，预测表现也不能证明所学边具有因果含义。
原文摘要
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.