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In this paper, we investigate the Gaussian graphical model inference problemin a novel setting that we call erose measurements, referring to irregularlymeasured or observed data. For graphs, this results in different node pairshaving vastly different sample sizes which frequently arises in dataintegration, genomics, neuroscience, and sensor networks. Existing workscharacterize the graph selection performance using the minimum pairwise samplesize, which provides little insights for erosely measured data, and no existinginference method is applicable. We aim to fill in this gap by proposing thefirst inference method that characterizes the different uncertainty levels overthe graph caused by the erose measurements, named GI-JOE (Graph Inference whenJoint Observations are Erose). Specifically, we develop an edge-wise inferencemethod and an affiliated FDR control procedure, where the variance of each edgedepends on the sample sizes associated with corresponding neighbors. We provestatistical validity under erose measurements, thanks to careful localizededge-wise analysis and disentangling the dependencies across the graph.Finally, through simulation studies and a real neuroscience data example, wedemonstrate the advantages of our inference methods for graph selection fromerosely measured data.

Graphical Model Inference with Erosely Measured Data