Toward Metrics for Differentiating Out-of-Distribution Sets

Vanilla CNNs, as uncalibrated classifiers, suffer from classifying out-of-distribution (OOD) samples nearly as confidently as in-distribution samples, making them indistinguishable from each other. To tackle this challenge, some recent works have demonstrated the gains of leveraging readily accessible OOD sets for training end-to-end calibrated CNNs. However, a critical question remains unanswered in these works: how to select an OOD set, among the available OOD sets, for training such CNNs that induces high detection rates on unseen OOD sets? We address this pivotal question through the use of Augmented-CNN (A-CNN) involving an explicit rejection option. We first provide a formal definition to precisely differentiate OOD sets for the purpose of selection. As using this definition incurs a huge computational cost, we propose novel metrics, as a computationally efficient tool, for characterizing OOD sets in order to select the proper one. In a series of experiments on several image and audio benchmarks, we show that training an A-CNN with an OOD set identified by our metrics (called A-CNN$^{\star}$) leads to remarkable detection rate of unseen OOD sets while maintaining in-distribution generalization performance, thus demonstrating the viability of our metrics for identifying the proper OOD set. Furthermore, we show that A-CNN$^{\star}$ outperforms state-of-the-art OOD detectors across different benchmarks.