How Many and Which Training Points Would Need to be Removed to Flip this Prediction?

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• github.com/ecielyang/smallest_set
  OfficialIn papernone★ 1

Abstract

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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