Contrastive Pessimistic Likelihood Estimation
As we discussed in the previous chapter, in many real-life problems, it's cheaper to retrieve unlabeled samples, rather than correctly labeled ones. For this reason, many researchers have worked to find out the best strategies to carry out a semi-supervised classification that could outperform its supervised counterpart. The idea is to train a classifier with a few labeled samples and then improve its accuracy after adding weighted unlabeled samples. One of the best results is the CPLE algorithm, proposed by Loog (in Loog M., Contrastive Pessimistic Likelihood Estimation for Semi-Supervised Classification, arXiv:1503.00269, 2015).
Before we can explain this algorithm, it's necessary to define Platt scaling. If we have a labeled dataset (X, Y) containing N samples, it's possible to define the log-likelihood cost function of a generic estimator, as follows:
After training the model, it should be possible to determine...