Lasso regression is similar to ridge regression, but instead uses the $\ell_1$ regularization penalty. This has the effect of setting some coefficient estimates to exactly zero for the least influential variables, which leads to models only including a subset of variables. This results in a sparse solution, which is a kind of feature selection. The parameter $\lambda$ controls the amount of $\ell_1$ regularization. The prediction formula is the same as ordinary least squares (OLS), but it minimizes the following objective function: $RSS_{LASSO}(\beta_{j}, \beta_{0}) = \sum_{i=1}^{n} ({y}_{i}-{\beta}_{0}-\sum_{j=1}^{p}{\beta}_{j}{x}_{ij})^2 +\lambda\sum_{j=1}^{p}\vert{\beta}_{j}\vert=RSS+\lambda\sum_{j=1}^{p}\vert{\beta}_{j}\vert$