1.Sage Bionetworks,Seatle,USA;2.Department of Mathematics,Michigan State University,East Lansing,USA;3.Departments of Statistical Science, Computer Science, and Mathematics,Duke University,Durham,USA
Abstract:
We consider the problem of hierarchical or multitask modeling where we simultaneously learn the regression function and the
underlying geometry and dependence between variables. We demonstrate how the gradients of the multiple related regression
functions over the tasks allow for dimension reduction and inference of dependencies across tasks jointly and for each task
individually. We provide Tikhonov regularization algorithms for both classification and regression that are efficient and
robust for high-dimensional data, and a mechanism for incorporating a priori knowledge of task (dis)similarity into this framework.
The utility of this method is illustrated on simulated and real data.