sklearn.linear model.Lasso System

A sklearn.linear_model.Lasso System is a linear least-squares L1-regularized regression system within sklearn.linear_model (that implements a LASSO algorithm to solve a LASSO task).

• Context:
  • Usage:

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

2) Create design matrix X and response vector Y

3) Create Lasso Regression object: lasso=Lasso(alpha=alpha[,fit_intercept=True, normalize=False,...])

4) Choose method(s):

• Fit model with coordinate descent: lasso.fit(X, Y[, check_input]))
• Predict Y using the linear model with estimated coefficients: Y_pred = lasso.predict(X)
• Return coefficient of determination (R^2) of the prediction: lasso.score(X,Y[, sample_weight=w])
• Compute elastic net path with coordinate descent: lasso.path(X, y[, l1_ratio, eps, n_alphas,...])
• Get estimator parameters: lasso.get_params([deep])
• Set estimator parameters: lasso.set_params(**params)

• Example(s):
  • 10-fold sklearn Boston data evaluation [1]

Input:	Output:
from sklearn.cross_validation import KFold from sklearn.linear_model import Lasso from sklearn.datasets import load_boston boston = load_boston() x = np.array([np.concatenate((v,[1])) for v in boston.data]) y = boston.target lasso = Lasso(fit_intercept=True, alpha=0.5) lasso.fit(x,y) p = lasso.predict(x) plot(p, y,'ro')
err = p-y total_error = np.dot(err,err) rmse_train = np.sqrt(total_error/len(p)) kf = KFold(len(x), n_folds=10) xval_err = 0 for train,test in kf: lasso.fit(x[train],y[train]) p = lasso.predict(x[test]) e = p-y[test] xval_err += np.dot(e,e) rmse_10cv = np.sqrt(xval_err/len(x))	Method: Lasso Regression RMSE on training set: 4.9141 RMSE on 10-fold CV: 5.7368

• Counter-Example(s)
  • sklearn.linear_model.LassoLars
  • sklearn.linear_model.LassoCV.
  • sklearn.linear_model.LassoLarsCV.
• See: LASSO Task, sklearn.decomposition.sparse_encode.sklearn.decomposition.sparse_encode, sklearn.linear_model.lars_path System, sklearn.

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References

2017a

• (Scikit Learn, 2017) ⇒ http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Lasso.html#sklearn.linear_model.Lasso
  • QUOTE: class sklearn.linear_model.Lasso(alpha=1.0, fit_intercept=True, normalize=False, precompute=False, copy_X=True, max_iter=1000, tol=0.0001, warm_start=False, positive=False, random_state=None, selection=’cyclic’)

Linear Model trained with L1 prior as regularizer (aka the Lasso)

The optimization objective for Lasso is:

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

Technically the Lasso model is optimizing the same objective function as the Elastic Net with l1_ratio=1.0 (no L2 penalty).

Read more in the User Guide.

2017b

• http://scikit-learn.org/stable/auto_examples/linear_model/plot_lasso_and_elasticnet.html#sphx-glr-auto-examples-linear-model-plot-lasso-and-elasticnet-py

2017c

• http://scikit-learn.org/stable/auto_examples/applications/plot_tomography_l1_reconstruction.html#sphx-glr-auto-examples-applications-plot-tomography-l1-reconstruction-py

2017D

• https://www.analyticsvidhya.com/blog/2016/01/complete-tutorial-ridge-lasso-regression-python/#four]

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