Resampling Methods - Part 3 - Estimation with Cross-Validation

Cross-validation is a statistical method used to estimate the skill of machine learning models. 

It is commonly used in applied machine learning to compare and select a model for a given predictive modeling problem because it is easy to understand, easy to implement, and results in skill estimates that generally have a lower bias than other methods. 

In this tutorial, you will discover a gentle introduction to the k-fold cross-validation procedure for estimating the skill of machine learning models. 

After completing this tutorial, you will know:

• That k-fold cross-validation is a procedure used to estimate the skill of the model on new data.
• There are common tactics that you can use to select the value of k for your dataset.
• There are commonly used variations on cross-validation such as stratified and repeated that are available in scikit-learn.

This tutorial is divided into 5 parts; they are:

• k-Fold Cross-Validation
• Configuration of k
• Worked Example
• Cross-Validation in Python
• Variations on Cross-Validation

1. k-Fold Cross-Validation

Cross-validation is a resampling procedure used to evaluate machine learning models on a limited data sample. 

The procedure has a single parameter called k that refers to the number of groups that a given data sample is to be split into. As such, the procedure is often called k-fold cross-validation. 

When a specific value for k is chosen, it may be used in place of k in the reference to the model, such as k=10 becoming 10-fold cross-validation.

Cross-validation is primarily used in applied machine learning to estimate the skill of a machine learning model on unseen data. 

That is, to use a limited sample in order to estimate how the model is expected to perform in general when used to make predictions on data not used during the training of the model. 

It is a popular method because it is simple to understand and because it generally results in a less biased or less optimistic estimate of the model skill than other methods, such as a simple train/test split.

1. Shuffle the dataset randomly.
2. Split the dataset into k groups
3. For each unique group:
1. Take the group as a hold out or test data set
2. Take the remaining groups as a training data set
3. Fit a model on the training set and evaluate it on the test set
4. Retain the evaluation score and discard the model
4. Summarize the skill of the model using the sample of model evaluation scores
   

This approach involves randomly dividing the set of observations into k groups, or folds, of approximately equal size. The first fold is treated as a validation set, and the method is fit on the remaining k − 1 folds.

The results of a k-fold cross-validation run are often summarized with the mean of the model skill scores. It is also good practice to include a measure of the variance of the skill scores, such as the standard deviation or standard error.

2. Configuration of k

The k value must be chosen carefully for your data sample. A poorly chosen value for k may result in a mis-representative idea of the skill of the model, such as a score with a high variance or a high bias.

Three common tactics for choosing a value for k are as follows:

• Representative: The value for k is chosen such that each train/test group of data samples is large enough to be statistically representative of the broader dataset.
• k=10: The value for k is fixed to 10, a value that has been found through experimentation to generally result in a model skill estimate with low bias a modest variance.
• k=n: The value for k is fixed to n, where n is the size of the dataset to give each test sample an opportunity to be used in the hold out dataset. This approach is called leave-one-out cross-validation.

A value of k=10 is very common in the field of applied machine learning, and is recommend if you are struggling to choose a value for your dataset.

3. Worked Example

To make the cross-validation procedure concrete, let’s look at a worked example. Imagine we have a data sample with 6 observations:

    [0.1, 0.2, 0.3, 0.4, 0.5, 0.6]

Here, we will use a value of k = 3.

That means we will shuffle the data and then split the data into 3 groups. Because we have 6 observations, each group will have an equal number of 2 observations.

    Fold1: [0.5, 0.2]
    Fold2: [0.1, 0.3]
    Fold3: [0.4, 0.6]

Three models are trained and evaluated with each fold given a chance to be the held out test set. For example:

    Model1: Trained on Fold1 + Fold2, Tested on Fold3

    Model2: Trained on Fold2 + Fold3, Tested on Fold1

    Model3: Trained on Fold1 + Fold3, Tested on Fold2

The skill scores are collected for each model and summarized for use.

4. Cross-Validation in Python

The scikit-learn library provides an implementation that will split a given data sample up. The KFold() scikit-learn class can be used.

For example, we can create an instance that splits a dataset into 3 folds, shuffles prior to the split, and uses a value of 1 for the pseudorandom number generator.

# scikit-learn k-fold cross-validation
from numpy import array
from sklearn.model_selection import KFold
# data sample
data = array([0.1, 0.2, 0.3, 0.4, 0.5, 0.6])
# prepare cross validation
kfold = KFold(3, True, 1)
# enumerate splits
for train, test in kfold.split(data):
print('train: %s, test: %s' % (data[train], data[test]))

-----Result-----

train: [0.1 0.4 0.5 0.6], test: [0.2 0.3]
train: [0.2 0.3 0.4 0.6], test: [0.1 0.5]
train: [0.1 0.2 0.3 0.5], test: [0.4 0.6]

5. Variations on Cross-Validation

There are a number of variations on the k-fold cross-validation procedure. Four commonly used variations are as follows:

• Train/Test Split: Taken to one extreme, k may be set to 1 such that a single train/test split is created to evaluate the model.
• LOOCV: Taken to another extreme, k may be set to the total number of observations in the dataset such that each observation is given a chance to be the held out of the dataset. This is called leave-one-out cross-validation, or LOOCV for short.
• Stratified: The splitting of data into folds may be governed by criteria such as ensuring that each fold has the same proportion of observations with a given categorical value, such as the class outcome value. This is called stratified cross-validation.
• Repeated: This is where the k-fold cross-validation procedure is repeated n times, where importantly, the data sample is shuffled prior to each repetition, which results in a different split of the sample.

The scikit-learn library provides a suite of cross-validation implementation. You can see the full list in the Model Selection API.