Lasso Regression

Definition

$\begin{array}{rl}{\hat{\beta }}_{\text{lasso}}& =\underset{\beta }{\mathrm{argmin}}(\mathbf{y}-\mathbf{X}\beta {)}^{⊺}(\mathbf{y}-\mathbf{X}\beta )+\lambda ||\beta ||\\ & =\underset{\beta }{\mathrm{argmin}}(\mathbf{y}-\mathbf{X}\beta {)}^{⊺}(\mathbf{y}-\mathbf{X}\beta ),\text{subject to}||\beta ||\le c\end{array}$

Lasso model assume that the coefficients of the model are sparse.