Generalized SMO Algorithm for SVM-Based Multitask Learning

Exploiting additional information to improve traditional inductive learning is an active research area in machine learning. In many supervised-learning applications, training data can be naturally separated into several groups, and incorporating this group information into learning may improve generalization. Recently, Vapnik proposed a general approach to formalizing such problems, known as "learning with structured data" and its support vector machine (SVM) based optimization formulation called SVM+. Liang and Cherkassky showed the connection between SVM+ and multitask learning (MTL) approaches in machine learning, and proposed an SVM-based formulation for MTL called SVM+ MTL for classification. Training the SVM+ MTL classifier requires the solution of a large quadratic programming optimization problem which scales as O(n(3)) with sample size n. So there is a need to develop computationally efficient algorithms for implementing SVM+ MTL. This brief generalizes Platt's sequential minimal optimization (SMO) algorithm to the SVM+ MTL setting. Empirical results show that, for typical SVM+ MTL problems, the proposed generalized SMO achieves over 100 times speed-up, in comparison with general-purpose optimization routines.