稀疏图的选择性推断：基于邻域选择
Selective Inference for Sparse Graphs via Neighborhood Selection
AI总结：
针对稀疏图邻域选择估计缺乏不确定性度量的问题，提出基于外部随机化的选择性推断方法，精确调整边选择事件，实现有效推断，提升功效与精度。
摘要：
邻域选择是一种广泛用于估计稀疏精度矩阵支撑集的方法，有助于确定无向图模型中的条件依赖结构。然而，仅报告估计图的点估计而缺乏伴随的不确定性估计，可能导致可重复性较差。在心理学等领域，缺乏可重复性是一个主要关注点，因此对能够解决此问题的方法的需求日益增长。本文聚焦于高斯图模型。我们引入了一种选择性推断方法，为精度矩阵中选定的（非零）条目附加不确定性估计，并决定哪些估计出的边应包含在图中。我们的方法对边的选择提供了精确的调整，该调整与随机矩阵的Wishart密度相乘后，可产生有效的选择性推断。通过使用外部添加的随机化变量，我们的调整易于计算，只需计算选择事件的概率，该概率等价于若干符号约束，并在节点级回归之间解耦。通过模拟实验以及一项旨在研究心理健康的移动健康试验的应用，我们证明了我们的选择性推断方法能带来更高的功效和改进的估计精度。
英文摘要：
Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point estimates for the estimated graph can result in poor replicability without accompanying uncertainty estimates. In fields such as psychology, where the lack of replicability is a major concern, there is a growing need for methods that can address this issue. In this paper, we focus on the Gaussian graphical model. We introduce a selective inference method to attach uncertainty estimates to the selected (nonzero) entries of the precision matrix and decide which of the estimated edges must be included in the graph. Our method provides an exact adjustment for the selection of edges, which when multiplied with the Wishart density of the random matrix, results in valid selective inferences. Through the use of externally added randomization variables, our adjustment is easy to compute, requiring us to calculate the probability of a selection event, that is equivalent to a few sign constraints and that decouples across the nodewise regressions. Through simulations and an application to a mobile health trial designed to study mental health, we demonstrate that our selective inference method results in higher power and improved estimation accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
