Error control and Neyman–Pearson classification with buffered probability and support vectors

WWe utilize buffered probability of exceedance (bPOE) to introduce a new formulation for classification with asymmetric error control inspired by the Neyman–Pearson (NP) paradigm. This paper proposes a computationally efficient large margin classifier with the same generalization benefits as support vector machines in high-dimensional feature spaces that is also a provably optimal convex approximation of the traditional NP classification problem. Our approach is not proposed as an approximation heuristic based on convex surrogates. Called buffered NP (bNP) classification, our approach is a new counterpart formulation to NP classification derived from bPOE, a novel quantification of uncertainty. While NP classification minimizes the false positive rate (FPR) while controlling the false negative rate (FNR), our approach considers the severity of both false positives and negatives by utilizing two new performance metrics called the buffered false negative rate (bFNR) and buffered false positive rate (bFPR). This new approach has two major advantages. First, the bNP classification problem accounts for the severity of different error types, revealing aspects of classifier performance hidden by the FNR and FPR. Second, the bNP classification problem can be reduced to convex, sometimes linear, programming. In addition, we show that we can naturally introduce regularization, creating a margin maximizing bNP classification problem that shares strong connections with SVM’s. Along with margin maximization, our formulation can use the kernel trick for non-linear classification, with the optimal classifier also having a support vector expansion effectively controlling classifier complexity in high dimensional feature spaces.