Multitarget Sparse Latent Regression

Multitarget regression has recently generated intensive popularity due to its ability to simultaneously solve multiple regression tasks with improved performance, while great challenges stem from jointly exploring inter-target correlations and input–output relationships. In this paper, we propose multitarget sparse latent regression (MSLR) to simultaneously model intrinsic intertarget correlations and complex nonlinear input–output relationships in one single framework. By deploying a structure matrix, the MSLR accomplishes a latent variable model which is able to explicitly encode intertarget correlations via $\ell _{2,1}$ -norm-based sparse learning; the MSLR naturally admits a representer theorem for kernel extension, which enables it to flexibly handle highly complex nonlinear input-output relationships; the MSLR can be solved efficiently by an alternating optimization algorithm with guaranteed convergence, which ensures efficient multitarget regression. Extensive experimental evaluation on both synthetic data and six greatly diverse real-world data sets shows that the proposed MSLR consistently outperforms the state-of-the-art algorithms, which demonstrates its great effectiveness for multivariate prediction.