Prerequisites: L2 and L1 regularization
This article aims to implement the L2 and L1 regularization for Linear regression using the Ridge and Lasso modules of the Sklearn library of Python.
Dataset – House prices dataset.
Step 1: Importing the required libraries
Python3
import pandas as pdimport numpy as npimport matplotlib.pyplot as pltfrom sklearn.linear_model import LinearRegression, Ridge, Lassofrom sklearn.model_selection import train_test_split, cross_val_scorefrom statistics import mean |
Step 2: Loading and cleaning the Data
Python3
# Changing the working location to the location of the datacd C:\Users\Dev\Desktop\Kaggle\House Prices# Loading the data into a Pandas DataFramedata = pd.read_csv('kc_house_data.csv')# Dropping the numerically non-sensical variablesdropColumns = ['id', 'date', 'zipcode']data = data.drop(dropColumns, axis = 1)# Separating the dependent and independent variablesy = data['price']X = data.drop('price', axis = 1)# Dividing the data into training and testing setX_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.25) |
Step 3: Building and evaluating the different models
a) Linear Regression:
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# Building and fitting the Linear Regression modellinearModel = LinearRegression()linearModel.fit(X_train, y_train)# Evaluating the Linear Regression modelprint(linearModel.score(X_test, y_test)) |
b) Ridge(L2) Regression:
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# List to maintain the different cross-validation scorescross_val_scores_ridge = []# List to maintain the different values of alphaalpha = []# Loop to compute the different values of cross-validation scoresfor i in range(1, 9): ridgeModel = Ridge(alpha = i * 0.25) ridgeModel.fit(X_train, y_train) scores = cross_val_score(ridgeModel, X, y, cv = 10) avg_cross_val_score = mean(scores)*100 cross_val_scores_ridge.append(avg_cross_val_score) alpha.append(i * 0.25)# Loop to print the different values of cross-validation scoresfor i in range(0, len(alpha)): print(str(alpha[i])+' : '+str(cross_val_scores_ridge[i])) |
From the above output, we can conclude that the best value of alpha for the data is 2.
Python3
# Building and fitting the Ridge Regression modelridgeModelChosen = Ridge(alpha = 2)ridgeModelChosen.fit(X_train, y_train)# Evaluating the Ridge Regression modelprint(ridgeModelChosen.score(X_test, y_test)) |
c) Lasso(L1) Regression:
Python3
# List to maintain the cross-validation scorescross_val_scores_lasso = []# List to maintain the different values of LambdaLambda = []# Loop to compute the cross-validation scoresfor i in range(1, 9): lassoModel = Lasso(alpha = i * 0.25, tol = 0.0925) lassoModel.fit(X_train, y_train) scores = cross_val_score(lassoModel, X, y, cv = 10) avg_cross_val_score = mean(scores)*100 cross_val_scores_lasso.append(avg_cross_val_score) Lambda.append(i * 0.25)# Loop to print the different values of cross-validation scoresfor i in range(0, len(alpha)): print(str(alpha[i])+' : '+str(cross_val_scores_lasso[i])) |
From the above output, we can conclude that the best value of lambda is 2.
Python3
# Building and fitting the Lasso Regression ModellassoModelChosen = Lasso(alpha = 2, tol = 0.0925)lassoModelChosen.fit(X_train, y_train)# Evaluating the Lasso Regression modelprint(lassoModelChosen.score(X_test, y_test)) |
Step 4: Comparing and Visualizing the results
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# Building the two lists for visualizationmodels = ['Linear Regression', 'Ridge Regression', 'Lasso Regression']scores = [linearModel.score(X_test, y_test), ridgeModelChosen.score(X_test, y_test), lassoModelChosen.score(X_test, y_test)]# Building the dictionary to compare the scoresmapping = {}mapping['Linear Regression'] = linearModel.score(X_test, y_test)mapping['Ridge Regression'] = ridgeModelChosen.score(X_test, y_test)mapping['Lasso Regression'] = lassoModelChosen.score(X_test, y_test)# Printing the scores for different modelsfor key, val in mapping.items(): print(str(key)+' : '+str(val)) |
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# Plotting the scoresplt.bar(models, scores)plt.xlabel('Regression Models')plt.ylabel('Score')plt.show() |
