Reverse testing: an efficient framework to select amongst classifiers under sample selection bias

One of the most important assumptions made by many classification algorithms is that the training and test sets are drawn from the same distribution, i.e., the so-called "stationary distribution assumption" that the future and the past data sets are identical from a probabilistic standpoint. In many domains of real-world applications, such as marketing solicitation, fraud detection, drug testing, loan approval, sub-population surveys, school enrollment among others, this is rarely the case. This is because the only labeled sample available for training is biased in different ways due to a variety of practical reasons and limitations. In these circumstances, traditional methods to evaluate the expected generalization error of classification algorithms, such as structural risk minimization, ten-fold cross-validation, and leave-one-out validation, usually return poor estimates of which classification algorithm, when trained on biased dataset, will be the most accurate for future unbiased dataset, among a number of competing candidates. Sometimes, the estimated order of the learning algorithms' accuracy could be so poor that it is not even better than random guessing. Therefore,a method to determine the most accurate learner is needed for data mining under sample selection bias for many real-world applications. We present such an approach that can determine which learner will perform the best on an unbiased test set, given a possibly biased training set, in a fraction of the computational cost to use cross-validation based approaches.