Gaussian Graphical Learning via PSD Constraint for Blockwise Missing Multimodal Data

Abstract

Gaussian graphical models, estimated via precision matrices, are popular for uncovering underlying conditional dependencies among variables, yet the case of multimodal data with blockwise missing remains unaddressed. We propose a novel method, Direct Sparse Graphical Learning for Multimodal Data (DSGL), to handle this issue using only observed data. The DSGL consists of two stages: constructing a pilot estimator for the covariance matrix without imputation as an admissible input for GLASSO; and estimating the DSGL precision matrix via GLASSO with repeated cross-validation tuning. We further propose a thresholded variant to address false-positive edges, a common issue in high-dimensional data. We establish theoretical properties for DSGL with respect to element-wise deviation and its ability to recover the true graphical structure. In simulations and an Alzheimer’s Disease Neuroimaging Initiative (ADNI) application, DSGL outperforms imputation-based and other competing approaches, yielding more accurate graph estimation and lower Frobenius-norm error.