Disproportion among class priors is encountered in a large number of domains making conventional learning algorithms less effective in predicting samples belonging to the minority classes. We aim at developing a reconstruction rule suited to multiclass skewed data. In performing this task we use the classification reliability that conveys useful information on the goodness of classification acts. In the framework of One-per-Class decomposition scheme we design a novel reconstruction rule, Reconstruction Rule by Selection, which uses classifiers reliabilities, crisp labels and a-priori distributions to compute the final decision. Tests show that system performance improves using this rule rather than using well-established reconstruction rules. We investigate also the rules in the Error Correcting Output Code (ECOC) decomposition framework. Inspired by a statistical reconstruction rule designed for the One-per-Class and Pair-Wise Coupling decomposition approaches, we have developed a rule that applies softmax regression on reliability outputs in order to estimate the final classification. Results show that this choice improves the performances with respect to the existing statistical rule and to well-established reconstruction rules. On the topic of reliability estimation we notice that small attention has been given to efficient posteriors estimation in the boosting framework. On this reason we develop an efficient posteriors estimator by boosting Nearest Neighbors. Using Universal Nearest Neighbours classifier we prove that a sub-class of surrogate losses exists, whose minimization brings simple and statistically efficient estimators for Bayes posteriors.
