These are slides from a presentation I did at USC on two papers related to sparse feature selection in multi-task learning with linear models.
I did an in-class presentation on two papers on multitask learning. Each paper covered a different approach to feature selection for linear regression with multivariate responses under the assumption of sparsity. Obozinski et al (2011) imposes sparsity in the union of the supports by imposing a group lasso penalty on each feature across every response (corresponding to rows of the coefficient matrix). Chen et al (2012) instead examine the singular value decomposition (SVD) of the coefficient matrix and impose sparsity in the left and right singular vectors in each SVD layer (relaxing orthogonality to achieve sparsity). Check out my slides for a summary of these papers, plus I included my notes I referred to during the presentation. Feel free to reach out with any questions!
Papers:
Obozinski, Guillaume; Wainwright, Martin J.; Jordan, Michael I. Support union recovery in high-dimensional multivariate regression. Ann. Statist. 39 (2011), no. 1, 1--47. doi:10.1214/09-AOS776. https://projecteuclid.org/euclid.aos/1291388368
Chen, K. , Chan, K. and Stenseth, N. C. (2012), Reduced rank stochastic regression with a sparse singular value decomposition. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 74: 203-221. doi:10.1111/j.1467-9868.2011.01002.x