What is cross-validation and what are its types, explain it with example ?
What is Cross-Validation?
Cross-validation is a statistical method used to estimate the skill of machine learning models. It is primarily used to assess how the results of a statistical analysis will generalize to an independent data set. The primary goal is to prevent overfitting by testing the model’s ability to perform on unseen data.
Why Use Cross-Validation?
Cross-validation is particularly useful in scenarios where the sample size is limited. In such cases, leveraging the available data fully by using it for both training and testing (in turns) ensures a better estimate of the model’s performance than using a simple train/test split.
Types of Cross-Validation
Several methods of cross-validation provide different benefits depending on the situation:
1. K-Fold Cross-Validation
Description: The data set is divided into K equal subsets, and the holdout method is repeated K times. Each time, one of the K subsets is used as the test set (the "validation set") and the other K-1 subsets are put together to form a training set. The error estimation is averaged over all K trials to get the total effectiveness of the model.
Example: If you have 200 data points and you choose 5-fold cross-validation, each fold contains 40 data points. The model is trained 5 times, each time using a different group of 40 data points as the validation set and the remaining 160 as the training set.
2. Stratified K-Fold Cross-Validation
Description: Similar to K-fold but it ensures each fold of the dataset has the same proportion of observations with a given categorical label. This is particularly useful for imbalanced datasets.
Example: In a binary classification with an imbalanced dataset where 90% of the data are of class 0 and 10% are of class 1, stratified K-fold ensures each fold has 90% of data from class 0 and 10% from class 1.
3. Leave-One-Out Cross-Validation (LOOCV)
Description: This is a specific case of K-fold cross-validation where K equals the number of data points in the dataset. That is, for N data points, N separate times, the model is trained on all the data except for one point and tested on that single left-out observation.
Example: If your dataset consists of 100 samples, the LOOCV approach would involve using 99 samples for training and 1 sample for testing. This is repeated such that each sample gets to be used in the test set once.
4. Leave-P-Out Cross-Validation
Description: This method leaves out P observations for validation and uses the remaining ones for training. Unlike LOOCV, it doesn't exhaustively consider all possible ways to leave out P examples, because this would become computationally infeasible for large P.
Example: With 100 samples, choosing P=3 means each training set is created by leaving out 3 samples, creating many possible training/testing sets.
5. Time Series Cross-Validation
Description: A variant important for time series data. Instead of random sampling, the data is split along the time dimension. The training sets are always prior in time to the test sets.
Example: If you have monthly sales data for 5 years, you may train on the first 3 years and validate on the next year, and test on the final year, ensuring temporal order is respected.
Benefits and When to Use Each
K-Fold Cross-Validation: Most commonly used because it provides a good compromise between computational efficiency and the benefits of resampling.
Stratified K-Fold Cross-Validation: Best for dealing with small or imbalanced datasets where the class distribution is important.
LOOCV: Useful when the dataset is very small, and you need to maximize the use of your data. However, it can be computationally expensive.
Leave-P-Out Cross-Validation: Generally impractical for large datasets but can be useful for small datasets where exhaustive approaches are feasible.
Time Series Cross-Validation: Essential for time-dependent data, where conventional methods might leak information from the future into the training process.