diff --git a/doc/modules/linear_model.rst b/doc/modules/linear_model.rst index b68f6232b3194..637cf0f8a5601 100644 --- a/doc/modules/linear_model.rst +++ b/doc/modules/linear_model.rst @@ -867,12 +867,20 @@ following cost function: .. math:: \min_{w} C \sum_{i=1}^n \left[-y_i \log(\hat{p}(X_i)) - (1 - y_i) \log(1 - \hat{p}(X_i))\right] + r(w). -We currently provide four choices for the regularization term: - -#. `penalty=None` for :math:`r(w) = 0` -#. `penalty=l1` for the pure :math:`\ell_1`-penalty :math:`r(w) = \|w\|_1` -#. :math:`\ell_2,\, r(w) = \frac{1}{2}\|w\|_2^2 = \frac{1}{2}w^T w` -#. ElasticNet, :math:`r(w) = \frac{1 - \rho}{2}w^T w + \rho \|w\|_1` +We currently provide four choices for the regularization term :math:`r(w)` via +the `penalty` argument: + ++----------------+-------------------------------------------------+ +| penalty | :math:`r(w)` | ++================+=================================================+ +| `None` | :math:`0` | ++----------------+-------------------------------------------------+ +| :math:`\ell_1` | :math:`\|w\|_1` | ++----------------+-------------------------------------------------+ +| :math:`\ell_2` | :math:`\frac{1}{2}\|w\|_2^2 = \frac{1}{2}w^T w` | ++----------------+-------------------------------------------------+ +| `ElasticNet` | :math:`\frac{1 - \rho}{2}w^T w + \rho \|w\|_1` | ++----------------+-------------------------------------------------+ For ElasticNet, :math:`\rho` (which corresponds to the `l1_ratio` parameter) controls the strength of :math:`\ell_1` regularization vs. :math:`\ell_2`