Machine Learning Lesson of the Day – Cross-Validation

Validation is a good way to assess the predictive accuracy of a supervised learning algorithm, and the rule of thumb of using 70% of the data for training and 30% of the data for validation generally works well.  However, what if the data set is not very large, and the small amount of data for training results in high sampling error?  A good way to overcome this problem is K-fold cross-validation.

Cross-validation is best defined by describing its steps:

For each model under consideration,

  1. Divide the data set into K partitions.
  2. Designate the first partition as the validation set and designate the other partitions as the training set.
  3. Use training set to train the algorithm.
  4. Use the validation set to assess the predictive accuracy of the algorithm; the common measure of predictive accuracy is mean squared error.
  5. Repeat Steps 2-4 for the second partition, third partition, … , the (K-1)th partition, and the Kth partition.  (Essentially, rotate the designation of validation set through every partition.)
  6. Calculate the average of the mean squared error from all K validations.

Compare the average mean squared errors of all models and pick the one with the smallest average mean squared error as the best model.  Test all models on a separate data set (called the test set) to assess their predictive accuracies on new, fresh data.

If there are N data in the data set, and K = N, then this type of K-fold cross-validation has a special name: leave-one-out cross-validation (LOOCV).

There some trade-offs between a large and a small K.  The estimator for the prediction error from a larger K results in

  • less bias because of more data being used for training
  • higher variance because of the higher similarity and lower diversity between the training sets
  • slower computation because of more data being used for training

In The Elements of Statistical Learning (2009 Edition, Chapter 7, Page 241-243), Hastie, Tibshirani and Friedman recommend 5 or 10 for K.

Your thoughtful comments are much appreciated!

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