Abstract

We consider the problem of including additional knowledge in estimating sparse Gaussian graphical models (sGGMs) from aggregated samples, arising often in bioinformatics and neuroimaging applications. Previous joint sGGM estimators either fail to use existing knowledge or cannot scale-up to many tasks (large K) under a highdimensional (large p) situation. In this paper, we propose a novel Joint Elementary Estimator incorporating additional Knowledge (JEEK) to infer multiple related sparse Gaussian Graphical models from large-scale heterogeneous data. Using domain knowledge as weights, we design a novel hybrid norm as the minimization objective to enforce the superposition of two weighted sparsity constraints, one on the shared interactions and the other on the task-specific structural patterns. This enables JEEK to elegantly consider various forms of existing knowledge based on the domain at hand and avoid the need to design knowledgespecific optimization. JEEK is solved through a fast and entry-wise parallelizable solution that largely improves the computational efficiency of the state-of-the-art We conduct a rigorous statistical analysis showing that JEEK achieves the same convergence rate as the state-of-the-art estimators that are much harder to compute. Empirically, on multiple synthetic datasets and two real-world data, JEEK outperforms the speed of the state-ofarts significantly while achieving the same level of prediction accuracy.