Multi-task learning of Gaussian graphical models

We present multi-task structure learning for Gaussian graphical models. We discuss uniqueness and boundedness of the optimal solution of the maximization 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 l _∞ regularized quadratic minimization subprob-lems. We further show that this subprob-lem leads to the continuous quadratic knapsack problem, for which very efficient methods exist. Finally, we show promising results in a dataset that captures brain function of cocaine addicted and control subjects under conditions of monetary reward.