sklearn.linear model.Ridge

A sklearn.linear model.Ridge is a ridge regression system within sklearn.linear_model class.

• Context
  • Usage:

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

2) Create design matrix X and response vector Y

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

4) Choose method(s):

• Fit Ridge regression model: model.fit(X, Y[, check_input]))
• Predict Y using the linear model with estimated coefficients: Y_pred = model.predict(X)
• Return coefficient of determination (R^2) of the prediction: model.score(X,Y[, sample_weight=w])
• Get estimator parameters: model.get_params([deep])
• Set estimator parameters: model.set_params(**params)

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

Input:	Output:
from sklearn.linear_model import Ridge from sklearn.model_selection import cross_val_predict from sklearn.datasets import load_boston from sklearn.metrics import explained_variance_score, mean_squared_error import numpy as np import pylab as pl boston = load_boston() #Loading boston datasets x = boston.data # Creating Regression Design Matrix y = boston.target # Creating target dataset ridgereg= Ridge(alpha=0.5) # Create Ridge regression object with alpha=0.5 ridgereg.fit(x,y) # Fit linear regression yp = ridgereg.predict(x) # predicted values yp_cv = cross_val_predict(ridgereg, x, y, cv=10) #Calculation 10-Fold CV	(blue dots correspond to 10-Fold CV)
#Calculaton of RMSE and Explained Variances Evariance=explained_variance_score(y,yp) Evariance_cv=explained_variance_score(y,yp_cv) RMSE =np.sqrt(mean_squared_error(y,yp)) RMSECV =sqrt(mean_squared_error(y,yp_cv)_	Method: Ridge Regression RMSE on the dataset: 4.6857 RMSE on 10-fold CV: 5.8428 Explained Variance Regression Score on the dataset : 0.7399 Explained Variance Regression 10-fold CV: 0.5956

• Use of RidgeCV and LassoCV to set the regularization parameter

• Counter-Example(s)
  • sklearn.linear_model.Lasso
  • sklearn.linear_model.LinearRegression.
  • sklearn.linear_model.ARDRegression.
  • sklearn.linear_model.BayesianRidge.
  • sklearn.linear_model.ElasticNet.
  • sklearn.linear_model.HuberRegressor.
  • sklearn.linear_model.Lars.
• See: Ridge Regression Task, Regularization Task, Estimation Task, L2-Norm.

---

---

References

2017

• http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Ridge.html
  • QUOTE: class sklearn.linear_model.Ridge(alpha=1.0, fit_intercept=True, normalize=False, copy_X=True, max_iter=None, tol=0.001, solver=’auto’, random_state=None)

    Linear least squares with l2 regularization.

    This model solves a regression model where the loss function is the linear least squares function and regularization is given by the l2-norm. Also known as Ridge Regression or Tikhonov regularization. This estimator has built-in support for multi-variate regression (i.e., when y is a 2d-array of shape [n_samples, n_targets]).

---