Simultaneous and group-sparse multitask learning of gaussian graphical models

In this paper, we present `1,p multi-task structure learning for Gaussian graphical models. We discuss the uniqueness and boundedness of the optimal solution of the max-imization problem. A block coordinate descent method leads to a provably convergent algorithm that generates a sequence of positive definite solutions. Thus, we reduce the original problem into a sequence of strictly convex `p regularized quadratic minimization subproblems. We further show that this subproblem leads to the continuous quadratic knapsack problem for p = ∞ and to a separable version of the well-known quadratic trust-region problem for p = 2, for which very efficient methods exist. Finally, we show promising results in synthetic experiments as well as in two real-world datasets.