How Many and Which Training Points Would Need to be Removed to Flip this Prediction?
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We consider the problem of identifying a minimal subset of training data 𝒮_t such that if the instances comprising 𝒮_t had been removed prior to training, the categorization of a given test point x_t would have been different. Identifying such a set may be of interest for a few reasons. First, the cardinality of 𝒮_t provides a measure of robustness (if |𝒮_t| is small for x_t, we might be less confident in the corresponding prediction), which we show is correlated with but complementary to predicted probabilities. Second, interrogation of 𝒮_t may provide a novel mechanism for contesting a particular model prediction: If one can make the case that the points in 𝒮_t are wrongly labeled or irrelevant, this may argue for overturning the associated prediction. Identifying 𝒮_t via brute-force is intractable. We propose comparatively fast approximation methods to find 𝒮_t based on influence functions, and find that – for simple convex text classification models – these approaches can often successfully identify relatively small sets of training examples which, if removed, would flip the prediction.
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