Why do classifier accuracies show linear trends under distribution shift?
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Several recent studies observed that when classification models are evaluated on two different data distributions, the models' accuracies on one distribution are approximately a linear function of their accuracies on another distribution. We offer an explanation for these observations based on two assumptions that can be assessed empirically: (1) certain events have similar probabilities under the two distributions; (2) the probability that a lower accuracy model correctly classifies a data point sampled from one distribution when a higher accuracy model classifies it incorrectly is small.
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