## Machine Learning and Applied Statistics Lesson of the Day – Sensitivity and Specificity

To evaluate the predictive accuracy of a binary classifier, two useful (but imperfect) criteria are sensitivity and specificity.

Sensitivity is the proportion of truly positives cases that were classified as positive; thus, it is a measure of how well your classifier identifies positive cases.  It is also known as the true positive rate.  Formally,

$\text{Sensitivity} = \text{(Number of True Positives)} \ \div \ \text{(Number of True Positives + Number of False Negatives)}$

Specificity is the proportion of truly negative cases that were classified as negative; thus, it is a measure of how well your classifier identifies negative cases.  It is also known as the true negative rate.  Formally,

$\text{Specificity} = \text{(Number of True Negatives)} \ \div \ \text{(Number of True Negatives + Number of False Positives)}$

## 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.

## Machine Learning Lesson of the Day – Using Validation to Assess Predictive Accuracy in Supervised Learning

Supervised learning puts a lot of emphasis on building a model that has high predictive accuracy.  Validation is a good method for assessing a model’s predictive accuracy.

Validation is the use of one part of your data set to build your model and another part of your data set to assess the model’s predictive accuracy.  Specifically,

1. split your data set into 2 sets: a training set and a validation set
2. use the training set to fit your model (e.g. LASSO regression)
3. use the predictors in the validation set to predict the targets
4. use some error measure (e.g mean squared error) to assess the differences between the predicted targets and the actual targets.

A good rule of thumb is to use 70% of your data for training and 30% of your data for your validation.

You should do this for several models (e.g. several different values of the penalty parameter in LASSO regression).  The model with the lowest mean squared error can be judged as the best model.

I highly encourage you to test your models on a separate data set – called a test set – from the same population or probability distribution and assess their predictive accuracies on the test set.  This is a good way to check for any overfitting in your models.