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In recent years, a certain type of problems have become of interest where onewants to query a trained classifier. Specifically, one wants to find theclosest instance to a given input instance such that the classifier's predictedlabel is changed in a desired way. Examples of these ``inverse classification''problems are counterfactual explanations, adversarial examples and modelinversion. All of them are fundamentally optimization problems over the inputinstance vector involving a fixed classifier, and it is of interest to achievea fast solution for interactive or real-time applications. We focus on solvingthis problem efficiently for two of the most widely used classifiers: logisticregression and softmax classifiers. Owing to special properties of thesemodels, we show that the optimization can be solved in closed form for logisticregression, and iteratively but extremely fast for the softmax classifier. Thisallows us to solve either case exactly (to nearly machine precision) in aruntime of milliseconds to around a second even for very high-dimensionalinstances and many classes.

Inverse classification with logistic and softmax classifiers: efficient optimization