SparseRegression is a Julia package which combines JuliaML primitives to implement high-performance algorithms for fitting linear models.
The objective function that SparseRegression can solve takes the form:
where $f$ is a loss function, $J$ is a penalty or regularization function, the $w_i$'s are nonnegative observation weights and the $\lambda_j$'s are nonnegative element-wise regularization parameters. Many models take this form:
|Lasso Regression||$(y_i - x_i^T\beta)^2$||$|\beta_j|$|
|Ridge Regression||$(y_i - x_i^T\beta)^2$||$\beta_j^2$|
|SVM||$max(0, 1 - y_i x_i^T\beta)$||$\beta_j^2$|
The three core JuliaML packages that SparseRegression brings together are: