in the context of this chapter, the training set is composed by all labelled examples that are provided for constructing a classifier. The test set is composed by the new unlabelled patterns whose classes should be predicted by the classifier
Óscar Pérez (Universidad Autónoma de Madrid, Spain) and Manuel Sánchez-Montañés (Universidad Autónoma de Madrid, Spain)
Machine learning has provided powerful algorithms that automatically generate predictive models from experience. One specific technique is
supervised learning, where the machine is trained to predict a desired output for each input pattern
x. This chapter will focus on
classification, that is, supervised learning when the output to predict is a class label. For instance predicting whether a patient in a hospital will develop cancer or not. In this example, the class label
c is a variable having two possible values, “cancer” or “no cancer”, and the input pattern
x is a vector containing patient data (e.g. age, gender, diet, smoking habits, etc.). In order to construct a proper predictive model, supervised learning methods require a set of examples
xi together with their respective labels c
i. This dataset is called the “training set”. The constructed model is then used to predict the labels of a set of new cases
xj called the “test set”. In the cancer prediction example, this is the phase when the model is used to predict cancer in new patients.
One common assumption in supervised learning algorithms is that the statistical structure of the training and test datasets are the same (Hastie, Tibshirani & Friedman, 2001). That is, the test set is assumed to have the same attribute distribution p(
x) and same class distribution p(c|
x) as the training set. However, this is not usually the case in real applications due to different reasons. For instance, in many problems the training dataset is obtained in a specific manner that differs from the way the test dataset will be generated later. Moreover, the nature of the problem may evolve in time. These phenomena cause p
Tr(
x, c)
p
Test(
x, c), which can degrade the performance of the model constructed in training.
Here we present a new algorithm that allows to re-estimate a model constructed in training using the unlabelled test patterns. We show the convergence properties of the algorithm and illustrate its performance with an artificial problem. Finally we demonstrate its strengths in a heart disease diagnosis problem where the training set is taken from a different hospital than the test set.