Sparse group lasso and high dimensional multinomial classification
This work addresses high-dimensional classification problems, particularly for multinomial data, by providing an efficient and scalable implementation, though it is incremental as it builds on existing lasso methods.
The paper tackles the sparse group lasso optimization problem for high-dimensional multinomial classification by developing a coordinate gradient descent algorithm, which on three real data examples outperforms multinomial lasso with fewer features and similar run-time, scaling to problems with 500k parameters.
The sparse group lasso optimization problem is solved using a coordinate gradient descent algorithm. The algorithm is applicable to a broad class of convex loss functions. Convergence of the algorithm is established, and the algorithm is used to investigate the performance of the multinomial sparse group lasso classifier. On three different real data examples the multinomial group lasso clearly outperforms multinomial lasso in terms of achieved classification error rate and in terms of including fewer features for the classification. The run-time of our sparse group lasso implementation is of the same order of magnitude as the multinomial lasso algorithm implemented in the R package glmnet. Our implementation scales well with the problem size. One of the high dimensional examples considered is a 50 class classification problem with 10k features, which amounts to estimating 500k parameters. The implementation is available as the R package msgl.