Error control for support vector machines

In binary classi¯cation there are two types of errors, and in many applications
these may have very di®erent costs. We consider two learning frameworks that ad-
dress this issue: minimax classi¯cation, where we seek to minimize the maximum
of the false alarm and miss rates, and Neyman-Pearson (NP) classi¯cation, where
we seek to minimize the miss rate while ensuring the false alarm rate is less than a
speci¯ed level ®. We show that our approach, based on cost-sensitive support vector
machines, signi¯cantly outperforms methods typically used in practice. Our results
also illustrate the importance of heuristics for improving the accuracy of error rate
estimation in this setting. We then reduce anomaly detection to NP classi¯cation
by considering a second class of points, allowing us to estimate minimum volume
sets using algorithms for NP classi¯cation. Comparing this approach with traditional
one-class methods, we ¯nd that our approach has several advantages.