基于最大似然的图模型选择性推断
Selective Inference in Graphical Models via Maximum Likelihood
AI总结：
该研究针对图套索推断边值函数时缺乏统计保证的问题，提出带随机化的选择性推断方法，通过条件最大似然实现有效区间估计与假设检验，效果优于数据拆分。
摘要：
图套索（graphical lasso）是拟合无向高斯图模型的广泛应用算法。然而，对于学习到的图中边值函数的推断，标准工具缺乏正式统计保证，如一类错误率的控制。我们提出一种选择性推断方法，用于经图套索选择并加入随机化后的渐近有效推断。我们通过对随机化变量的已知密度进行变量变换，得到选择事件条件下的选择性似然。该方法可利用条件最大似然估计器，对学习到的图中边值的广泛函数进行区间估计和假设检验。数值研究表明，引入少量随机化：（i）在模型选择质量上比数据拆分取得更好结果；（ii）在高维场景下确保区间长度有界，而数据拆分因推断样本有限存在功效低或未达到渐近状态的问题；（iii）支持对学习到的图中广泛推断目标的推断，包括偏相关、节点影响度量及节点间连通性度量。
英文摘要：
The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control of the type I error rate. We introduce a selective inference method for asymptotically valid inference after graphical lasso selection with added randomization. We obtain a selective likelihood, conditional on the event of selection, through a change of variable on the known density of the randomization variables. Our method enables interval estimation and hypothesis testing for a wide range of functionals of edge values in the learned graph using the conditional maximum likelihood estimator. Our numerical studies show that introducing a small amount of randomization: (i) achieves better results than data splitting in terms of model selection quality; (ii) ensures intervals of bounded length also in high-dimensional settings where data splitting suffers from low power or does not reach asymptotic regime due to limited samples for inference; (iii) enables inference for a wide range of inferential targets in the learned graph, including partial correlations and measures of node influence and connectivity between nodes.
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