sklearn.linear model.HuberRegressor

A sklearn.linear model.HuberRegressor is an Huber Regression System within sklearn.linear_model class.

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

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

2) Create design matrix X and response vector Y

3) Create Huber Regression object: Hreg=HuberRegressor([epsilon=1.35, max_iter=100, alpha=0.0001, warm_start=False, fit_intercept=True, tol=1e-05])

4) Choose method(s):

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

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

Input:

Output:

#Importing modules from sklearn.linear_model import HuberRegressor 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 Hreg= HuberRegressor(epsilon=1.0) # Create Huber regression object Hreg.fit(x,y) # predicted values #Calculaton of RMSE and Explained Variances yp_cv = cross_val_predict(Hreg, 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: Huber 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('Huber Regression, epsilon=1.0') pl.ylabel('real') pl.grid(True) pl.show()

(blue dots correspond to 10-Fold CV) Method: Huber Regression RMSE on the dataset: 5.1709 RMSE on 10-fold CV: 6.4916 Explained Variance Regression Score on the dataset: 0.6932 Explained Variance Regression 10-fold CV: 0.5027

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

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References

2017

• http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.HuberRegressor.html
  • QUOTE: class sklearn.linear_model.HuberRegressor(epsilon=1.35, max_iter=100, alpha=0.0001, warm_start=False, fit_intercept=True, tol=1e-05)

Linear regression model that is robust to outliers.

The Huber Regressor optimizes the squared loss for the samples where |(y - X'w) / sigma| < epsilon and the absolute loss for the samples where |(y - X'w) / sigma| > epsilon, where w and sigma are parameters to be optimized. The parameter sigma makes sure that if y is scaled up or down by a certain factor, one does not need to rescale epsilon to achieve the same robustness. Note that this does not take into account the fact that the different features of X may be of different scales.

This makes sure that the loss function is not heavily influenced by the outliers while not completely ignoring their effect.

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