grouplasso

Group Lasso is a statistical method used for feature selection and regularization in linear models. It extends the standard Lasso method by encouraging sparsity at the group level. Instead of selecting individual features, Group Lasso selects entire groups of features to be included or excluded from the model. This is particularly useful when features are naturally organized into meaningful groups, such as all features related to a specific gene or all variables within a particular experimental condition.

The core idea behind Group Lasso is to apply an L1 penalty not to individual coefficients, but to the Euclidean norm of the coefficients within each group. This means that if any feature within a group is selected, all features in that group are effectively brought into the model, and if a group is not selected, all its features are removed. This group-wise sparsity pattern can lead to more interpretable models and improved performance when group structure is present.

Group Lasso has found applications in various fields, including bioinformatics, where genes are often grouped by pathways, and in medical imaging, where voxels can be grouped by anatomical regions. The objective function minimized by Group Lasso typically includes a loss function (e.g., least squares for regression) and a regularization term that sums the L2 norms of coefficient vectors for each group, all scaled by a regularization parameter. This parameter controls the trade-off between model fit and sparsity.