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Modern neural networks are very powerful predictive models, but they are often incapable of recognizing when their predictions may be wrong. Closely related to this is the task of out-of-distribution detection, where a network must determine whether or not an input is outside of the set on which it is expected to safely perform. To jointly address these issues, we propose a method of learning confidence estimates for neural networks that is simple to implement and produces intuitively interpretable outputs. We demonstrate that on the task of out-of-distribution detection, our technique surpasses recently proposed techniques which construct confidence based on the network's output distribution, without requiring any additional labels or access to out-of-distribution examples. Additionally, we address the problem of calibrating out-of-distribution detectors, where we demonstrate that misclassified in-distribution examples can be used as a proxy for out-of-distribution examples.