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One measure of an estimator's robustness is the breakdown point, which tells us how many adversarial observations are necessary to make the estimator useless.

However, is there a notion of non-adversarial robustness? For example, say we are working in a situation where new observations come from a known distribution. What tools do we have to measure the robustness of current estimators under these new observations?

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You can measure aleatoric and epistemic uncertainty of the estimator. Additionally, you can measure whether a domain shift exists by computing a KL or JS divergence between two distributions.

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