From the video series: Introduction to machine learning with scikit-learn
Motivation: Need a way to choose between machine learning models
Initial idea: Train and test on the same data
Alternative idea: Train/test split
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from sklearn.datasets import load_iris
from sklearn.cross_validation import train_test_split
from sklearn.neighbors import KNeighborsClassifier
from sklearn import metrics
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# read in the iris data
iris = load_iris()
# create X (features) and y (response)
X = iris.data
y = iris.target
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# use train/test split with different random_state values
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=4)
# check classification accuracy of KNN with K=5
knn = KNeighborsClassifier(n_neighbors=5)
knn.fit(X_train, y_train)
y_pred = knn.predict(X_test)
print metrics.accuracy_score(y_test, y_pred)
Question: What if we created a bunch of train/test splits, calculated the testing accuracy for each, and averaged the results together?
Answer: That's the essense of cross-validation!
Diagram of 5-fold cross-validation:
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# simulate splitting a dataset of 25 observations into 5 folds
from sklearn.cross_validation import KFold
kf = KFold(25, n_folds=5, shuffle=False)
# print the contents of each training and testing set
print '{} {:^61} {}'.format('Iteration', 'Training set observations', 'Testing set observations')
for iteration, data in enumerate(kf, start=1):
print '{:^9} {} {:^25}'.format(iteration, data[0], data[1])
Advantages of cross-validation:
Advantages of train/test split:
cross_val_score function does this by defaultGoal: Select the best tuning parameters (aka "hyperparameters") for KNN on the iris dataset
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from sklearn.cross_validation import cross_val_score
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# 10-fold cross-validation with K=5 for KNN (the n_neighbors parameter)
knn = KNeighborsClassifier(n_neighbors=5)
scores = cross_val_score(knn, X, y, cv=10, scoring='accuracy')
print scores
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# use average accuracy as an estimate of out-of-sample accuracy
print scores.mean()
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# search for an optimal value of K for KNN
k_range = range(1, 31)
k_scores = []
for k in k_range:
knn = KNeighborsClassifier(n_neighbors=k)
scores = cross_val_score(knn, X, y, cv=10, scoring='accuracy')
k_scores.append(scores.mean())
print k_scores
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import matplotlib.pyplot as plt
%matplotlib inline
# plot the value of K for KNN (x-axis) versus the cross-validated accuracy (y-axis)
plt.plot(k_range, k_scores)
plt.xlabel('Value of K for KNN')
plt.ylabel('Cross-Validated Accuracy')
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Goal: Compare the best KNN model with logistic regression on the iris dataset
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# 10-fold cross-validation with the best KNN model
knn = KNeighborsClassifier(n_neighbors=20)
print cross_val_score(knn, X, y, cv=10, scoring='accuracy').mean()
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# 10-fold cross-validation with logistic regression
from sklearn.linear_model import LogisticRegression
logreg = LogisticRegression()
print cross_val_score(logreg, X, y, cv=10, scoring='accuracy').mean()
Goal: Select whether the Newspaper feature should be included in the linear regression model on the advertising dataset
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import pandas as pd
import numpy as np
from sklearn.linear_model import LinearRegression
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# read in the advertising dataset
data = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)
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# create a Python list of three feature names
feature_cols = ['TV', 'Radio', 'Newspaper']
# use the list to select a subset of the DataFrame (X)
X = data[feature_cols]
# select the Sales column as the response (y)
y = data.Sales
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# 10-fold cross-validation with all three features
lm = LinearRegression()
scores = cross_val_score(lm, X, y, cv=10, scoring='mean_squared_error')
print scores
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# fix the sign of MSE scores
mse_scores = -scores
print mse_scores
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# convert from MSE to RMSE
rmse_scores = np.sqrt(mse_scores)
print rmse_scores
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# calculate the average RMSE
print rmse_scores.mean()
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# 10-fold cross-validation with two features (excluding Newspaper)
feature_cols = ['TV', 'Radio']
X = data[feature_cols]
print np.sqrt(-cross_val_score(lm, X, y, cv=10, scoring='mean_squared_error')).mean()
Repeated cross-validation
Creating a hold-out set
Feature engineering and selection within cross-validation iterations
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from IPython.core.display import HTML
def css_styling():
styles = open("styles/custom.css", "r").read()
return HTML(styles)
css_styling()
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