Error rate control for classification rules in multiclass mixture models

TL;DR

This paper develops a framework for controlling classification error rates in multiclass mixture models, proposing optimal rules that improve over traditional MAP-based methods, demonstrated through simulations and real data.

Contribution

It introduces a novel approach to optimize classification regions in mixture models, including a multiclass FDR-like rule, enhancing error control and reducing conservativeness.

Findings

FDR-like rule outperforms thresholded MAP in error control

Optimal regions depend on the targeted error rate

Method validated on simulated and real datasets

Abstract

In the context of finite mixture models one considers the problem of classifying as many observations as possible in the classes of interest while controlling the classification error rate in these same classes. Similar to what is done in the framework of statistical test theory, different type I and type II-like classification error rates can be defined, along with their associated optimal rules, where optimality is defined as minimizing type II error rate while controlling type I error rate at some nominal level. It is first shown that finding an optimal classification rule boils down to searching an optimal region in the observation space where to apply the classical Maximum A Posteriori (MAP) rule. Depending on the misclassification rate to be controlled, the shape of the optimal region is provided, along with a heuristic to compute the optimal classification rule in practice. In particular, a multiclass FDR-like optimal rule is defined and compared to the thresholded MAP rules that is used in most applications. It is shown on both simulated and real datasets that the FDR-like optimal rule may be significantly less conservative than the thresholded MAP rule.