15_cross_validation_nb.py

# # Cross-validation for parameter tuning, model selection, and feature selection

# ## Agenda
# - What is the drawback of using the **train/test split** procedure for model evaluation?
# - How does **K-fold cross-validation** overcome this limitation?
# - How can cross-validation be used for selecting **tuning parameters**, choosing between **models**, and selecting **features**?
# - What are some possible **improvements** to cross-validation?


# ## Review of model evaluation procedures

# **Motivation:** Need a way to choose between machine learning models
# - Goal is to estimate likely performance of a model on **out-of-sample data**

# **Initial idea:** Train and test on the same data
# - But, maximizing **training accuracy** rewards overly complex models which **overfit** the training data

# **Alternative idea:** Train/test split
# - Split the dataset into two pieces, so that the model can be trained and tested on **different data**
# - **Testing accuracy** is a better estimate than training accuracy of out-of-sample performance
# - But, it provides a **high variance** estimate since changing which observations happen to be in the testing set can significantly change testing accuracy

from sklearn.datasets import load_iris
from sklearn.cross_validation import train_test_split
from sklearn.neighbors import KNeighborsClassifier
from sklearn import metrics

# read in the iris data
iris = load_iris()

# create X (features) and y (response)
X = iris.data
y = iris.target

# 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!


# ## Steps for K-fold cross-validation

# 1. Split the dataset into K **equal** partitions (or "folds").
# 2. Use fold 1 as the **testing set** and the union of the other folds as the **training set**.
# 3. Calculate **testing accuracy**.
# 4. Repeat steps 2 and 3 K times, using a **different fold** as the testing set each time.
# 5. Use the **average testing accuracy** as the estimate of out-of-sample accuracy.

# 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])

# - Dataset contains **25 observations** (numbered 0 through 24)
# - 5-fold cross-validation, thus it runs for **5 iterations**
# - For each iteration, every observation is either in the training set or the testing set, **but not both**
# - Every observation is in the testing set **exactly once**


# ## Comparing cross-validation to train/test split

# Advantages of **cross-validation:**
# - More accurate estimate of out-of-sample accuracy
# - More "efficient" use of data (every observation is used for both training and testing)

# Advantages of **train/test split:**
# - Runs K times faster than K-fold cross-validation
# - Simpler to examine the detailed results of the testing process


# ## Cross-validation recommendations

# 1. K can be any number, but **K=10** is generally recommended
# 2. For classification problems, **stratified sampling** is recommended for creating the folds
#     - Each response class should be represented with equal proportions in each of the K folds
#     - scikit-learn's `cross_val_score` function does this by default

# ## Cross-validation example: parameter tuning
# **Goal:** Select the best tuning parameters (aka "hyperparameters") for KNN on the iris dataset

from sklearn.cross_validation import cross_val_score

# 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

# use average accuracy as an estimate of out-of-sample accuracy
print scores.mean()

# 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

# plot the value of K for KNN (x-axis) versus the cross-validated accuracy (y-axis)
import matplotlib.pyplot as plt
plt.plot(k_range, k_scores)
plt.xlabel('Value of K for KNN')
plt.ylabel('Cross-Validated Accuracy')


# ## Cross-validation example: model selection
# **Goal:** Compare the best KNN model with logistic regression on the iris dataset

# 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()

# 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()


# ## Cross-validation example: feature selection
# **Goal**: Select whether the Newspaper feature should be included in the linear regression model on the advertising dataset

import pandas as pd
import numpy as np
from sklearn.linear_model import LinearRegression

# read in the advertising dataset
data = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)

# 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

# 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

# fix the sign of MSE scores
mse_scores = -scores
print mse_scores

# convert from MSE to RMSE
rmse_scores = np.sqrt(mse_scores)
print rmse_scores

# calculate the average RMSE
print rmse_scores.mean()

# 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()


# ## Improvements to cross-validation

# **Repeated cross-validation**
# - Repeat cross-validation multiple times (with **different random splits** of the data) and average the results
# - More reliable estimate of out-of-sample performance by **reducing the variance** associated with a single trial of cross-validation

# **Creating a hold-out set**
# - "Hold out" a portion of the data **before** beginning the model building process
# - Locate the best model using cross-validation on the remaining data, and test it **using the hold-out set**
# - More reliable estimate of out-of-sample performance since hold-out set is **truly out-of-sample**

# **Feature engineering and selection within cross-validation iterations**
# - Normally, feature engineering and selection occurs **before** cross-validation
# - Instead, perform all feature engineering and selection **within each cross-validation iteration**
# - More reliable estimate of out-of-sample performance since it **better mimics** the application of the model to out-of-sample data