statsmodels.regression.linear_model.OLS.fit_regularized¶
method

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
 methodstring
‘elastic_net’ and ‘sqrt_lasso’ are currently implemented.
 alphascalar 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_paramsarraylike
Starting values for
params
. profile_scalebool
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.
 refitbool
If True, the model is refit using only the variables that have nonzero coefficients in the regularized fit. The refitted model is not regularized.
 distributedbool
If True, the model uses distributed methods for fitting, will raise an error if True and partitions is None.
 generatorfunction
generator used to partition the model, allows for handling of out of memory/parallel computing.
 partitionsscalar
The number of partitions desired for the distributed estimation.
 thresholdscalar or arraylike
The threshold below which coefficients are zeroed out, only used for distributed estimation
 Returns
 A RegularizedResults instance.
Notes
The elastic net uses a combination of L1 and L2 penalties. The implementation closely follows the glmnet package in R.
The function that is minimized is:
\[0.5*RSS/n + alpha*((1L1\_wt)*params_2^2/2 + L1\_wt*params_1)\]where RSS is the usual regression sum of squares, n is the sample size, and \(*_1\) and \(*_2\) are the L1 and L2 norms.
For WLS and GLS, the RSS is calculated using the whitened endog and exog data.
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:
 maxiterint
Maximum number of iterations
 cnvrg_tolfloat
Convergence threshold for line searches
 zero_tolfloat
Coefficients below this threshold are treated as zero.
The square root lasso approach is a variation of the Lasso that is largely selftuning (the optimal tuning parameter does not depend on the standard deviation of the regression errors). If the errors are Gaussian, the tuning parameter can be taken to be
alpha = 1.1 * np.sqrt(n) * norm.ppf(1  0.05 / (2 * p))
where n is the sample size and p is the number of predictors.
The square root lasso uses the following keyword arguments:
 zero_tolfloat
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.
A Belloni, V Chernozhukov, L Wang (2011). Squareroot Lasso: pivotal recovery of sparse signals via conic programming. Biometrika 98(4), 791806. https://arxiv.org/pdf/1009.5689.pdf