Commonly, Deep Neural Networks (DNNs) generalize well on samples drawn from a distribution similar to that of the training set. However, DNNs predictions are brittle and unreliable when the test samples are drawn from a dissimilar distribution. This presents a major concern for deployment in real-world applications, where such behavior may come at a great cost -- as in the case of autonomous vehicles or healthcare applications. This paper frames the Out Of Distribution (OOD) detection problem in DNN as a statistical hypothesis testing problem. Unlike previous OOD detection heuristics, our framework is guaranteed to maintain the false positive rate (detecting OOD as in-distribution) for test data. We build on this framework to suggest a novel OOD procedure based on low-order statistics. Our method achieves comparable or better than state-of-the-art results on well-accepted OOD benchmarks without retraining the network parameters -- and at a fraction of the computational cost.
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