MMT: A Matlab Library for Multi-Task Learning
MMT is a Matlab toolbox implementing the multi-task Lasso models, including: (i) the Lasso; (ii) the standard multi-task Lasso, i.e. the group Lasso; (iii) the structured input-output multi-task Lasso, a.k.a. the two-graph guided multi-task Lasso proposed in . The last case (iii) subsumes the special cases: tree-guided and the feature-graph guided multi-task Lasso. The core optimization algorithm for solving this model is developed in C to enhance greater computational efficiency. In particular, current scalability of the coefficient matrix that has been tested for MMT is 104*104! The structured input-output multi-task Lasso model is well-suited for addressing the expression quantitative trait loci (eQTL) mapping problems which are of the intrinsic high-dimensional nature. Details can be found in .
Input: an (n*p) regression matrix X, an (n*K) response matrix Y, an input graph G1 on X and an output graph G2 on Y, representing the prior structures on the columns of X and Y, respectively, regularization parameters λ1 and λ2 for the two prior graphs, and an (optional) initial guess of the coefficient matrix.
Output: a (p*K) estimated sparse coefficient matrix B.
 A two-graph guided multi-task Lasso approach for eQTL mapping. Xiaohui Chen, Xinghua Shi, Xing Xu, Zhiyong Wang, Ryan E. Mills, Charles Lee, Jinbo Xu. (2012) International Conference on Artificial Intelligence and Statistics (AISTATS’12). JMLR link