sklearn.linear model.BayesianRidge

A sklearn.linear_model.BayesianRidge is a Bayesian Ridge Regression System within sklearn.linear_model class.

• AKA: BayesianRidge, linear_model.BayesianRidge.
• Context
  • Usage:

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

2) Create design matrix X and response vector Y

3) Create BayesianRidge object: BRreg=BayesianRidge([n_iter=300, tol=0.001, alpha_1=1e-06, alpha_2=1e-06, lambda_1=1e-06, lambda_2=1e-06, compute_score=False, fit_intercept=True, normalize=False, copy_X=True, verbose=False])

4) Choose method(s):

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

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

Input:

Output:

#Importing modules from sklearn.linear_model import BayesianRidge 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 BRreg= BayesianRidge() # Create BR regression object BRreg.fit(x,y) # predicted values #Calculaton of RMSE and Explained Variances yp_cv = cross_val_predict(BRreg, x, y, cv=10) #Calculation 10-Fold CV 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) # Printing Results print('Method: BayesianRidge Regression') print('RMSE on the dataset: %.4f' %RMSE) print('RMSE on 10-fold CV: %.4f' %RMSECV) print('Explained Variance Regression Score on the dataset: %.4f' %Evariance) print('Explained Variance Regression 10-fold CV: %.4f' %Evariance_cv) #plotting real vs predicted data pl.figure(1) pl.plot(yp, y,'ro') pl.plot(yp_cv, y,'bo', alpha=0.25, label='10-folds CV') pl.xlabel('predicted') pl.title('BR Regression') pl.ylabel('real') pl.grid(True) pl.show()

(blue dots correspond to 10-Fold CV) Method: BayesianRidge Regression RMSE on the dataset: 4.7641 RMSE on 10-fold CV: 5.8463 Explained Variance Regression Score on the dataset: 0.7311 Explained Variance Regression 10-fold CV: 0.5952

• 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, Regularization Task, Ridge Regression Task, Bayesian Analysis.

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References

2017

• http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.BayesianRidge.html
  • QUOTE: class sklearn.linear_model.BayesianRidge(n_iter=300, tol=0.001, alpha_1=1e-06, alpha_2=1e-06, lambda_1=1e-06, lambda_2=1e-06, compute_score=False, fit_intercept=True, normalize=False, copy_X=True, verbose=False)

    Bayesian ridge regression

    Fit a Bayesian ridge model and optimize the regularization parameters lambda (precision of the weights) and alpha (precision of the noise).

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