基于联合图形马蹄先验的可扩展多网络推断
Scalable Multiple Network Inference with the Joint Graphical Horseshoe
AI总结：
针对图形马蹄先验在高维多网络推断中计算效率低的问题，提出可扩展ECM算法与联合图形马蹄估计器，实现跨网络信息借用并提升估计精度与可扩展性。
摘要：
网络模型是用于建模复杂关联的有用工具。若假设高斯图形模型，条件独立性由数据逆协方差（精度）矩阵的非零项决定。贝叶斯图形马蹄（graphical horseshoe）估计器为精度矩阵推断提供了一个稳健且灵活的框架，因为它引入了局部的、边特定的参数，从而防止非零非对角元素的过度收缩。然而，对于诸如统计组学等许多应用而言，当前基于吉布斯采样（Gibbs sampling）的实现在高维情况下计算效率低下，甚至不可行。此外，图形马蹄方法仅针对单一网络进行了公式化，而人们对可能共享共同结构的多数据集网络分析的兴趣日益增长。我们提出：(i) 一种可扩展的期望条件最大化（ECM）算法，用于在图形马蹄先验下获得精度矩阵的后验众数；以及 (ii) 一种新颖的联合图形马蹄估计器，该估计器跨多个相关网络借用信息以改进估计。我们在模拟数据和真实组学数据上表明，我们的单网络 ECM 方法比现有的图形马蹄吉布斯实现更具可扩展性，同时达到相同的精度水平。我们还表明，我们的联合网络方法成功地利用了网络之间共享的边特定信息，同时仍保留差异，在任何网络相似度水平上都优于最先进的方法。
英文摘要：
Network models are useful tools for modelling complex associations. If a Gaussian graphical model is assumed, conditional independence is determined by the non-zero entries of the inverse covariance (precision) matrix of the data. The Bayesian graphical horseshoe estimator provides a robust and flexible framework for precision matrix inference, as it introduces local, edge-specific parameters which prevent over-shrinkage of non-zero off-diagonal elements. However, for many applications such as statistical omics, the current implementation based on Gibbs sampling becomes computationally inefficient or even unfeasible in high dimensions. Moreover, the graphical horseshoe has only been formulated for a single network, whereas interest has grown in the network analysis of multiple data sets that might share common structures. We propose (i) a scalable expectation conditional maximisation (ECM) algorithm for obtaining the posterior mode of the precision matrix in the graphical horseshoe, and (ii) a novel joint graphical horseshoe estimator, which borrows information across multiple related networks to improve estimation. We show, on both simulated and real omics data, that our single-network ECM approach is more scalable than the existing graphical horseshoe Gibbs implementation, while achieving the same level of accuracy. We also show that our joint-network proposal successfully leverages shared edge-specific information between networks while still retaining differences, outperforming state-of-the-art methods at any level of network similarity.
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。
