LASSO Cross-Validation System

A LASSO Cross-Validation System is a Regression System that implements a LASSO CV Algorithm to solve a LASSO CV Task.

• AKA: LASSO CV System.
• Context:
  • It ranges from being a LASSO Regression System to being a Cross-Validation System.
• Example(s):
  • sklearn.linear_model.LassoCV [1].
    • Cross-validation on diabetes Dataset Exercise
    • Feature selection using SelectFromModel and LassoCV
• Counter-Example(s):
  • LASSO Regression System.
  • LASSO-LARS CV System.
  • LASSO-LARS IC System.
  • Multi-Task Lasso System.
  • ElasticNet System.
• See: Cross-Validation Task, L1-Norm.

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References

2017A

• (Scikit Learn, 2017) ⇒ http://scikit-learn.org/stable/modules/linear_model.html#using-cross-validation Retrieved:2017-09-17
  • QUOTE: scikit-learn exposes objects that set the Lasso alpha parameter by cross-validation: LassoCV and LassoLarsCV. LassoLarsCV</a> is based on the Least Angle Regression algorithm explained below.

    For high-dimensional datasets with many collinear regressors, LassoCV is most often preferable. However, LassoLarsCV has the advantage of exploring more relevant values of alpha parameter, and if the number of samples is very small compared to the number of features, it is often faster than LassoCV.

2017B

• (Scikit Learn, 2017) ⇒ http://scikit-learn.org/stable/modules/grid_search.html
  • QUOTE: 3.2.4.1. Model specific cross-validation

    Some models can fit data for a range of values of some parameter almost as efficiently as fitting the estimator for a single value of the parameter. This feature can be leveraged to perform a more efficient cross-validation used for model selection of this parameter.

    The most common parameter amenable to this strategy is the parameter encoding the strength of the regularizer. In this case we say that we compute the regularization path of the estimator.

Here is the list of such models:

 :: linear_model.ElasticNetCV([l1_ratio, eps,...]), Elastic Net model with iterative fitting along a regularization path;

linear_model.LarsCV([fit_intercept, ...]), Cross-validated Least Angle Regression model

linear_model.LassoCV([eps, n_alphas, ...]), Lasso linear model with iterative fitting along a regularization path;

linear_model.LassoLarsCV([fit_intercept, ...]), Cross-validated Lasso, using the LARS algorithm

linear_model.LogisticRegressionCV([Cs, ...]), Logistic Regression CV (aka logit, MaxEnt) classifier.

linear_model.MultiTaskElasticNetCV([...]), Multi-task L1/L2 ElasticNet with built-in cross-validation.

linear_model.MultiTaskLassoCV([eps, ...]), Multi-task L1/L2 Lasso with built-in cross-validation.

linear_model.OrthogonalMatchingPursuitCV([...]), Cross-validated Orthogonal Matching Pursuit model (OMP)

linear_model.RidgeCV([alphas, ...]), Ridge regression with built-in cross-validation.

linear_model.RidgeClassifierCV([alphas, ...]), Ridge classifier with built-in cross-validation.

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