A Latent Multilayer Graphical Model For Complex, Interdependent Systems

Networks have been extensively used and have provided novel insights across a wide variety of research areas. However, many real-world systems are, in fact, a "network of networks", or a multilayer network, which interact as components of a larger multimodal system. A major difficulty in this multilayer framework is the estimation of interlayer edges or connections. In this work, we propose a new estimation method, called multilayer sparse + low-rank inverse covariance estimation (multiSLICE), which estimates the interlayer edges. multiSLICE bridges latent variable Gaussian graphical methods with multilayer networks, offering a flexible framework for modeling processes with irregular sampling and heterogeneous graph structures. We develop an effective algorithm to compute the estimator. We also establish theoretical conditions for the recoverability of the joint space, analyze how interlayer interactions influence joint parameter estimation, and provide theoretical bounds on their relationships. Finally, we rigorously evaluate our method on both simulated and multimodal neuroimaging data, demonstrating improvements over state-of-the-art approaches. All the relevant R code implementing the method in the article is available on GitHub. n Yes No Yes Yes No No Yes No Yes p No Yes No No Yes Yes Yes Yes Yes Table 1: A summary of methods in columns with year of publication. Entries indicate whether the approach can handle different sample sizes (n) or different node sets (p) across modalities.