Regularization for supervised learning via the "hubNet" procedure

We propose a new method for supervised learning. The hubNet procedure fits a hub-based graphical model to the predictors, to estimate the amount of "connection" that each predictor has with other predictors. This yields a set of predictor weights that are then used in a regularized regression such as the lasso or elastic net. The resulting procedure is easy to implement, can sometimes yields higher prediction accuracy that the lasso, and can give insights into the underlying structure of the predictors. HubNet can also be generalized seamlessly to other supervised problems such as regularized logistic regression (and other GLMs), Cox's proportional hazards model, and nonlinear procedures such as random forests and boosting. We prove some recovery results under a specialized model and illustrate the method on real and simulated data.