Convex factorization machine for toxicogenomics prediction

We introduce the convex factorization machine (CFM), which is a convex variant of the widely used Factorization Machines (FMs). Specifically, we employ a linear+quadratic model and regularize the linear term with the l₂-regularizer and the quadratic term with the trace norm regularizer. Then, we formulate the CFM optimization as a semidefinite programming problem and propose an efficient optimization procedure with Hazan's algorithm. A key advantage of CFM over existing FMs is that it can find a globally optimal solution, while FMs may get a poor locally optimal solution since the objective function of FMs is non-convex. In addition, the proposed algorithm is simple yet effective and can be implemented easily. Finally, CFM is a general factorization method and can also be used for other factorization problems, including multi-view matrix factorization and tensor completion problems, in various domains including toxicogenomics and bioinformatics. Through synthetic and traditionally used movielens datasets, we first show that the proposed CFM achieves results competitive to FMs. We then show in a toxicogenomics prediction task that CFM predicts the toxic outcomes of a collection of drugs better than a state-of-the-art tensor factorization method.