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We consider the problem of identifying a minimal subset of training data$\mathcal{S}_t$ such that if the instances comprising $\mathcal{S}_t$ had beenremoved prior to training, the categorization of a given test point $x_t$ wouldhave been different. Identifying such a set may be of interest for a fewreasons. First, the cardinality of $\mathcal{S}_t$ provides a measure ofrobustness (if $|\mathcal{S}_t|$ is small for $x_t$, we might be less confidentin the corresponding prediction), which we show is correlated with butcomplementary to predicted probabilities. Second, interrogation of$\mathcal{S}_t$ may provide a novel mechanism for contesting a particular modelprediction: If one can make the case that the points in $\mathcal{S}_t$ arewrongly labeled or irrelevant, this may argue for overturning the associatedprediction. Identifying $\mathcal{S}_t$ via brute-force is intractable. Wepropose comparatively fast approximation methods to find $\mathcal{S}_t$ basedon influence functions, and find that -- for simple convex text classificationmodels -- these approaches can often successfully identify relatively smallsets of training examples which, if removed, would flip the prediction.

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