The Lasso is a widely used method for feature selection in machine learning and statistics. It uses an L1 regularizer to induce sparsity in a linear model. The Elastic Net is similar to the Lasso, and uses a regularizer that is a mix between L2 and L1 penalties. It also produces sparse solutions, but is designed to select groups of collinear variables together, rather than in competition with each other. We describe these methodologies, and the popular R "glmnet" package that implements them. We also mention some newer Python packages, and demonstrate the techniques using several applications.
