Hands-On Machine Learning for Algorithmic Trading

How lasso regression works

The lasso, known as basis pursuit in signal processing, also shrinks the coefficients by adding a penalty to the sum of squares of the residuals, but the lasso penalty has a slightly different effect. The lasso penalty is the sum of the absolute values of the coefficient vector, which corresponds to its L¹ norm. Hence, the lasso estimate is defined by:

Similarly to ridge regression, the inputs need to be standardized. The lasso penalty makes the solution nonlinear, and there is no closed-form expression for the coefficients as in ridge regression. Instead, the lasso solution is a quadratic programming problem and ...