Multi-Class Classification with Asymmetric Error Control for Medical Disease Diagnosis

There is a growing need for asymmetric error control in medical disease diagnosis because the cost of a false negative may greatly exceed the cost of a false positive. This paper aims to extend the asymmetric error control achieved using the Neyman-Pearson (NP) Lemma in binary classification to multiclass classification. The NP oracle inequalities for binary classes are not immediately applicable for the multiclass NP classification, leading to a multi-step procedure to extend the algorithm in the context of multiple classes. Firstly, a hierarchical order of severity for misclassification for each class is maintained and the most critical classes identified. Secondly, the NP methods are applied to classify the most critical class versus the rest, and then the NP methods are applied to the next most severe class in the list versus the rest until a label is assigned. This approach is used to construct a novel tree-based classifier that enables asymmetric error control for multiclass classification and is evaluated on a cardiac arrhythmia dataset, where missing certain types of arrhythmia have more severe consequences than missing others. The results show that we are able to control the number of false negatives for the most critical classes in the multiclass classification problem.