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 inter-layer 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. Finally, all the relevant R code implementing the method in the article is available on [GitHub](https://github.com/mondrus96/multiSLICE).

Graphical models have been extensively used in, and provided novel insights across, a wide variety of research areas. Most current graph estimation methods assume a sparse structure. However, a sparse-only assumption is limiting and unrealistic in practice, hence sparse and low-rank forms have been suggested. In this work, we propose a new estimation method called sparse low-rank inverse covariance estimation (SLICE), which is a direct approach to jointly estimate the sparse and latent components of a Gaussian graphical model. SLICE utilizes a simple regularization term to ensure accurate estimates that are congruent with the covariance matrix. We derive an efficient and generalizable pseudo expectation maximization (EM) algorithm to solve for this estimator. Simulation and neuroimaging studies demonstrate the improvement of our SLICE approach over current state-of-the-art methods.

In this work, we introduce the R package fabisearch, available on the Comprehensive R Archive Network (CRAN), which implements an original change point detection method for multivariate high-dimensional time series data and a new interactive, 3-dimensional, brain-specific network visualization capability in a flexible, stand-alone function. Change point detection is a commonly used technique in time series analysis, capturing the dynamic nature in which many real-world processes function. With the ever increasing troves of multivariate high-dimensional time series data, especially in neuroimaging and finance, there is a clear need for scalable and data-driven change point detection methods. Currently, change point detection methods for multivariate high-dimensional data are scarce, with even less available in high-level, easily accessible software packages. fabisearch, which implements the factorized binary search (FaBiSearch) methodology, is a novel statistical method for detecting change points in the network structure of multivariate high-dimensional time series which employs non-negative matrix factorization (NMF), an unsupervised dimension reduction and clustering technique. Given the high computational cost of NMF, we implement the method in C++ code and use parallelization to reduce computation time. Further, we also utilize a new binary search algorithm to efficiently identify multiple change points and provide a new method for network estimation for data between change points. We show the functionality of the package and the practicality of the method by applying it to a neuroimaging and a finance data set. We also introduce an interactive, 3-dimensional, brain-specific network visualization capability in a flexible, stand-alone function. This function can be conveniently used with any node coordinate atlas, and nodes can be color coded according to community membership (if applicable). The output is an elegantly displayed network laid over a cortical surface, which can be rotated in the 3-dimensional space.