Classification using pattern probability estimators

We consider the problem of classification, where the data of the classes are generated i.i.d. according to unknown probability distributions. The goal is to classify test data with minimum error probability, based on the training data available for the classes. The Likelihood Ratio Test (LRT) is the optimal decision rule when the distributions are known. Hence, a popular approach for classification is to estimate the likelihoods using well known probability estimators, e.g., the Laplace and Good-Turing estimators, and use them in a LRT. We are primarily interested in situations where the alphabet of the underlying distributions is large compared to the training data available, which is indeed the case in most practical applications. We motivate and propose LRT´s based on pattern probability estimators that are known to achieve low redundancy for universal compression of large alphabet sources. While a complete proof for optimality of these decision rules is warranted, we demonstrate their performance and compare it with other well-known classifiers by various experiments on synthetic data and real data for text classification.