Collaborative regression

We consider the scenario where one observes an outcome variable and sets of features from multiple assays, all measured on the same set of samples. One approach that has been proposed for dealing with these type of data is "sparse multiple canonical correlation analysis" (sparse mCCA). All of the current sparse mCCA techniques are biconvex and thus have no guarantees about reaching a global optimum. We propose a method for performing sparse supervised canonical correlation analysis (sparse sCCA), a specific case of sparse mCCA when one of the datasets is a vector. Our proposal for sparse sCCA is convex and thus does not face the same difficulties as the other methods. We derive efficient algorithms for this problem that can be implemented with off the shelf solvers, and illustrate their use on simulated and real data.