This article focuses on covariance estimation for multi-study data. Popular approaches employ factor-analytic terms with shared and study-specific loadings that decompose the variance into (i) a shared low-rank component, (ii) study-specific low-rank components, and (iii) a diagonal term capturing idiosyncratic variability. Our proposed methodology estimates the latent factors via spectral decompositions, with a novel approach for separating shared and specific factors, and infers the factor loadings and residual variances via surrogate Bayesian regressions. The resulting posterior has a simple product form across outcomes, bypassing the need for Markov chain Monte Carlo sampling and facilitating parallelization. The proposed methodology has major advantages over current Bayesian competitors in terms of computational speed, scalability and stability while also having strong frequentist guarantees. The theory and methods also add to the rich literature on frequentist methods for factor models with shared and group-specific components of variation. The approximation error decreases as the sample size and the data dimension diverge, formalizing a blessing of dimensionality. We show favorable asymptotic properties, including central limit theorems for point estimators and posterior contraction, and excellent empirical performance in simulations. The methods are applied to integrate three studies on gene associations among immune cells.

翻译：本文聚焦于多研究数据的协方差估计。主流方法采用具有共享载荷和研究特定载荷的因子分析项，将方差分解为：(i) 共享低秩分量，(ii) 研究特定低秩分量，以及(iii) 捕捉特异变异的对角项。我们提出的方法通过谱分解估计潜在因子，采用新颖方法分离共享因子与特定因子，并通过替代贝叶斯回归推断因子载荷与残差方差。所得后验分布具有跨结果的简单乘积形式，无需马尔可夫链蒙特卡洛采样，便于并行化计算。该方法在计算速度、可扩展性和稳定性方面显著优于当前贝叶斯竞争方法，同时具备强大的频率学派保证。相关理论与方法亦丰富了具有共享变异分量与组特定变异分量的因子模型频率学派方法的文献体系。近似误差随样本量与数据维度发散而递减，形式化地体现了"维度福音"。我们证明了良好的渐近性质，包括点估计量的中心极限定理与后验收缩性，并在仿真中展现出优异的实证性能。该方法被应用于整合三项关于免疫细胞间基因关联的研究。