标题： 高维多研究多模态协变量增强广义因子模型 显示英文标题

标题： High-Dimensional Multi-Study Multi-Modality Covariate-Augmented Generalized Factor Model

摘要： 潜在因子模型将来自多个来源/研究或模态的数据进行整合，在各个学科中引起了广泛关注。然而，现有方法主要侧重于多研究整合或多模态整合，这使得它们在分析跨多个研究测量的多样化模态时显得不足。为了解决这一限制并满足实际需求，我们引入了一个高维广义因子模型，该模型能够无缝整合来自多个研究的多模态数据，同时还能适应额外的协变量。我们对可识别性条件进行了深入研究，以提高模型的可解释性。为了应对由四个大潜在随机矩阵引起的高维非线性整合的复杂性，我们利用变分下界通过采用变分后验分布来近似观察到的对数似然。通过对变分参数进行轮廓分析，我们使用M估计理论建立了模型参数估计量的渐近性质。此外，我们设计了一个计算高效的变分EM算法来执行估计过程，并制定了一种准则来确定研究共享和研究特异性因子的最佳数量。广泛的模拟研究和一个实际应用表明，所提出的方法在估计精度和计算效率方面显著优于现有方法。所提出方法的R包可在https://CRAN.R-project.org/package=MMGFM公开访问。 显示英文摘要

摘要： Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or multi-modality integration, rendering them insufficient for analyzing the diverse modalities measured across multiple studies. To address this limitation and cater to practical needs, we introduce a high-dimensional generalized factor model that seamlessly integrates multi-modality data from multiple studies, while also accommodating additional covariates. We conduct a thorough investigation of the identifiability conditions to enhance the model's interpretability. To tackle the complexity of high-dimensional nonlinear integration caused by four large latent random matrices, we utilize a variational lower bound to approximate the observed log-likelihood by employing a variational posterior distribution. By profiling the variational parameters, we establish the asymptotical properties of estimators for model parameters using M-estimation theory. Furthermore, we devise a computationally efficient variational EM algorithm to execute the estimation process and a criterion to determine the optimal number of both study-shared and study-specific factors. Extensive simulation studies and a real-world application show that the proposed method significantly outperforms existing methods in terms of estimation accuracy and computational efficiency. The R package for the proposed method is publicly accessible at https://CRAN.R-project.org/package=MMGFM.