高维高斯图回归模型的统计推断
Statistical Inference on High Dimensional Gaussian Graphical Regression Models
AI总结：
针对高维高斯图回归中统计推断未被探索的问题，提出基于多任务学习器的去偏估计量，通过新型投影技术降低计算成本，证明其渐近正态性可支撑有效统计推断，模拟和脑癌基因数据分析验证了实用性。
摘要：
高斯图回归已成为一种将高斯图模型的精度矩阵对协变量进行回归的强大方法，与传统高斯图模型不同，它有助于确定图如何受高维个体水平协变量调控，并能同时恢复群体水平和个体水平的图。为拟合该模型，多任务学习方法相比逐节点回归实现了更低的误差率。然而，由于高斯图回归问题的高复杂度和高维度，统计推断这一重要任务仍未被探索。我们提出一类基于多任务学习器的去偏估计量，用于高斯图回归中的统计推断。我们证明，去偏可以针对多任务学习器快速且独立地执行。在估计逆协方差矩阵的关键去偏步骤中，我们提出一种新颖的投影技术，可大幅降低优化中的计算成本，使其仅随样本量$n$缩放。我们证明，所提出的去偏估计量具有快速收敛速度，且渐近服从正态分布，从而可实现构建置信区间、进行假设检验等有效的统计推断。模拟研究证实了所提方法的实际效用，我们进一步将其应用于分析一项脑癌研究中的基因共表达图数据，揭示了有意义的生物学关联。
英文摘要：
Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are modulated by high dimensional subject-level covariates, and recover both the population-level and subject-level graphs. To fit the model, a multi-task learning approach achieves lower error rates compared to node-wise regressions. However, due to the high complexity and dimensionality of the Gaussian graphical regression problem, the important task of statistical inference remains unexplored. We propose a class of debiased estimators based on multi-task learners for statistical inference in Gaussian graphical regressions. We show that debiasing can be performed quickly and separately for the multi-task learners. In a key debiasing step that estimates the inverse covariance matrix, we propose a novel projection technique that dramatically reduces computational costs in optimization to scale only with the sample size $n$. We show that our debiased estimators enjoy a fast convergence rate and asymptotically follow a normal distribution, enabling valid statistical inference such as constructing confidence intervals and performing hypothesis testing. Simulation studies confirm the practical utility of the proposed approach, and we further apply it to analyze gene co-expression graph data from a brain cancer study, revealing meaningful biological relationships.
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。
