Graphical Model Inference with Erosely Measured Data

In this article, we investigate the Gaussian graphical model inference problem in a novel setting that we call <i>erose</i> measurements, referring to irregularly measured or observed data. For graphs, this results in different node pairs having vastly different sample sizes which frequently arises in data integration, genomics, neuroscience, and sensor networks. Existing works characterize the graph selection performance using the minimum pairwise sample size, which provides little insights for erosely measured data, and no existing inference method is applicable. We aim to fill in this gap by proposing the first inference method that characterizes the different uncertainty levels over the graph caused by the erose measurements, named GI-JOE (Graph Inference when Joint Observations are Erose). Specifically, we develop an edge-wise inference method and an affiliated FDR control procedure, where the variance of each edge depends on the sample sizes associated with corresponding neighbors. We prove statistical validity under erose measurements, thanks to careful localized edge-wise analysis and disentangling the dependencies across the graph. Finally, through simulation studies and a real neuroscience data example, we demonstrate the advantages of our inference methods for graph selection from erosely measured data. Supplementary materials for this article are available online.

本文针对一种被命名为不规则采样 (erose) 测量的新型场景下的高斯图模型 (Gaussian graphical model) 推断问题展开研究，此处的不规则采样测量指代观测数据存在不规则采集或测量的情形。对于图结构而言，该场景会导致不同节点对的样本量差异悬殊，这一现象在数据整合、基因组学、神经科学与传感器网络中十分常见。现有研究多通过最小节点对样本量来刻画图选择性能，但该指标难以有效解析不规则采样数据的内在特性，且目前尚无适配该场景的推断方法。为填补这一研究空白，本文提出了首个能够刻画由不规则采样所引发的图上不同不确定性水平的推断方法，命名为GI-JOE（联合观测不规则的图推断，Graph Inference when Joint Observations are Erose）。具体而言，我们开发了一种逐边推断方法及其配套的错误发现率 (False Discovery Rate, FDR) 控制流程，其中每条边的方差取决于其对应邻域所关联的样本量。得益于严谨的局域逐边分析以及对图内依赖关系的解耦处理，我们证明了该方法在不规则采样场景下的统计有效性。最后，通过模拟研究与真实神经科学数据实例，我们验证了所提推断方法在基于不规则采样数据开展图选择任务时的优势。本文补充材料可在线获取。