[FIXED] What is the objective function of LASSO in sklearn when we have multiple targets?

Issue

In sklearn's documentation, it says

The optimization objective for Lasso is:
(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1

I'm wondering if the shape of y is (n_targets, n_features), what is the definition of ||w||_1, where the shape of w in this case would be (n_features, n_targets).

Solution

As you might see from code or docs, in such a case the norm of w becomes its L_{2,1} norm. The euclidean norm of y - Xw becomes the Frobenius norm of the corresponding matrix.

Answered By - amiola