In classification applications, such as medical disease diagnosis, the cost of one type of error (false negative) could greatly outweigh the other (false positive) enabling the need of asymmetric error control. Due to this unique nature of the problem, traditional machine learning techniques, even with much improved accuracy, may not be ideal as they do not provide a way to control the false negatives below a certain threshold. To address this need, a classification algorithm that can provide asymmetric error control is proposed. The theoretical foundation for this algorithm is based on Neyman-Pearson (NP) Lemma and it is complemented with sample splitting and order statistics to pick a threshold that enables an upper bound on the number of false negatives. Additionally, this classifier addresses the imbalance of the data, which is common in medical datasets, by using Hellinger distance as the splitting criterion. This eliminates the need of sampling methods, which add complexity and the need for parameter selection. This approach is used to create a novel tree-based classifier that enables asymmetric error control. Applications, such as prediction of the severity of cardiac arrhythmia, require classification over multiple classes. The NP oracle inequalities for binary classes are not immediately applicable for the multiclass NP classification, leading to a multi-step procedure proposed in this dissertation to extend the algorithm in the context of multiple classes. This classifier is used in predicting various forms of cardiac disease for both binary and multi-class classification problems with not only comparable accuracy metrics but also with full control over the number of false negatives. Moreover, this research allows us to pick the threshold for the classifier in a data adaptive way. This dissertation also shows that this methodology can be extended to non medical applications that require classification with asymmetric error control.