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Conformal prediction (CP) is a wrapper around traditional machine learningmodels, giving coverage guarantees under the sole assumption ofexchangeability; in classification problems, for a chosen significance level$\varepsilon$, CP guarantees that the error rate is at most $\varepsilon$,irrespective of whether the underlying model is misspecified. However, theprohibitive computational costs of "full" CP led researchers to design scalablealternatives, which alas do not attain the same guarantees or statistical powerof full CP. In this paper, we use influence functions to efficientlyapproximate full CP. We prove that our method is a consistent approximation offull CP, and empirically show that the approximation error becomes smaller asthe training set increases; e.g., for $10^{3}$ training points the two methodsoutput p-values that are $<10^{-3}$ apart: a negligible error for any practicalapplication. Our methods enable scaling full CP to large real-world datasets.We compare our full CP approximation (ACP) to mainstream CP alternatives, andobserve that our method is computationally competitive whilst enjoying thestatistical predictive power of full CP.

Approximating Full Conformal Prediction at Scale via Influence Functions