A Latent Multilayer Graphical Model For Complex, Interdependent Systems
Martin Ondrus, Ivor Cribben, Yang Feng
Networks have been extensively used in and provided novel insights in 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 efficient computational algorithm to compute this estimator and establish theoretical conditions for the recoverability of the joint space and how inter-layer interactions influence joint parameter estimation, and we 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 experiments are available in an Anonymous Github.