sklearn.linear model.LassoLars

A sklearn.linear model.LassoLars is an LASSO-LARS System‎ within sklearn.linear_model class.

• Context:
  • Usage:

1) Import LassoLars model from scikit-learn : from sklearn.linear_model import LassoLars

2) Create design matrix X and response vector Y

3) Create LassoLars object: model=LassoLars([alpha=1.0, fit_intercept=True, verbose=False, normalize=True, precompute=’auto’,...])

4) Choose method(s):

• fit(X, y[, Xy]), fits the model using X, y as training data.
• get_params([deep]), gets parameters for this estimator.
• predict(X), predicts using the linear model
• score(X, y[, sample_weight]), returns the coefficient of determination R^2 of the prediction.
• set_params(**params), sets the parameters of this estimator.

• Example(s):
  • http://scikit-learn.org/stable/modules/linear_model.html#least-angle-regression

Input:	Output:
from sklearn import linear_model reg = linear_model.LassoLars(alpha=.1) reg.fit([[0, 0], [1, 1]], [0, 1]) reg.coef_	LassoLars(alpha=0.1, copy_X=True, eps=..., fit_intercept=True, fit_path=True, max_iter=500, normalize=True, positive=False, precompute='auto', verbose=False) array([ 0.717157..., 0. ])

• Counter-Example(s):
  • sklearn.linear model.LinearRegression
  • sklearn.linear_model.Lasso
  • sklearn.linear_model.Ridge.
  • sklearn.linear_model.ARDRegression.
  • sklearn.linear_model.ElasticNet.
  • sklearn.linear_model.HuberRegressor.
  • sklearn.linear_model.Lars.
• See: Regression System, Regressor, Cross-Validation Task, Ridge Regression Task, Bayesian Analysis.

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References

2017A

• (Scikit Learn, 2017)http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoLars.html
  • QUOTE: class sklearn.linear_model.LassoLars(alpha=1.0, fit_intercept=True, verbose=False, normalize=True, precompute=’auto’, max_iter=500, eps=2.2204460492503131e-16, copy_X=True, fit_path=True, positive=False)

Lasso model fit with Least Angle Regression a.k.a. Lars

It is a Linear Model trained with an L1 prior as regularizer.

The optimization objective for Lasso is:

(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1

2017B

• (Scikit Learn) ⇒ "1.1.8. LARS Lasso" http://scikit-learn.org/stable/modules/linear_model.html#lars-lasso Retrieved:2017-11-05
  • QUOTE: LassoLars is a lasso model implemented using the LARS algorithm, and unlike the implementation based on coordinate_descent, this yields the exact solution, which is piecewise linear as a function of the norm of its coefficients.

(...)

The algorithm is similar to forward stepwise regression, but instead of including variables at each step, the estimated parameters are increased in a direction equiangular to each one’s correlations with the residual.

Instead of giving a vector result, the LARS solution consists of a curve denoting the solution for each value of the L1 norm of the parameter vector. The full coefficients path is stored in the array coef_path_, which has size (n_features, max_features+1). The first column is always zero.

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