statsmodels.regression.linear_model.OLS.fit_regularized¶

OLS.
fit_regularized
(method='elastic_net', alpha=0.0, L1_wt=1.0, start_params=None, profile_scale=False, refit=False, **kwargs)[source]¶ Return a regularized fit to a linear regression model.
Parameters: method : string
Only the ‘elastic_net’ approach is currently implemented.
alpha : scalar or arraylike
The penalty weight. If a scalar, the same penalty weight applies to all variables in the model. If a vector, it must have the same length as params, and contains a penalty weight for each coefficient.
L1_wt: scalar
The fraction of the penalty given to the L1 penalty term. Must be between 0 and 1 (inclusive). If 0, the fit is a ridge fit, if 1 it is a lasso fit.
start_params : arraylike
Starting values for
params
.profile_scale : bool
If True the penalized fit is computed using the profile (concentrated) loglikelihood for the Gaussian model. Otherwise the fit uses the residual sum of squares.
refit : bool
If True, the model is refit using only the variables that have nonzero coefficients in the regularized fit. The refitted model is not regularized.
Returns: An array of coefficients, or a RegressionResults object of the
same type returned by
fit
.Notes
The elastic net approach closely follows that implemented in the glmnet package in R. The penalty is a combination of L1 and L2 penalties.
The function that is minimized is: ..math:
0.5*RSS/n + alpha*((1L1_wt)*params_2^2/2 + L1_wt*params_1)
where RSS is the usual regression sum of squares, n is the sample size, and and are the L1 and L2 norms.
Postestimation results are based on the same data used to select variables, hence may be subject to overfitting biases.
The elastic_net method uses the following keyword arguments:
 maxiter : int
 Maximum number of iterations
 cnvrg_tol : float
 Convergence threshold for line searches
 zero_tol : float
 Coefficients below this threshold are treated as zero.
References
Friedman, Hastie, Tibshirani (2008). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software 33(1), 122 Feb 2010.