Approximating Full Conformal Prediction at Scale via Influence Functions
This work addresses the scalability problem for practitioners needing reliable uncertainty quantification in machine learning, offering a computationally efficient alternative to full conformal prediction with minimal loss in accuracy.
The paper tackles the computational inefficiency of full conformal prediction by using influence functions to approximate it, achieving negligible approximation errors (e.g., p-values <10^{-3} apart for 10^3 training points) and enabling scaling to large datasets while maintaining statistical guarantees.
Conformal prediction (CP) is a wrapper around traditional machine learning models, giving coverage guarantees under the sole assumption of exchangeability; 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, the prohibitive computational costs of "full" CP led researchers to design scalable alternatives, which alas do not attain the same guarantees or statistical power of full CP. In this paper, we use influence functions to efficiently approximate full CP. We prove that our method is a consistent approximation of full CP, and empirically show that the approximation error becomes smaller as the training set increases; e.g., for $10^{3}$ training points the two methods output p-values that are $<10^{-3}$ apart: a negligible error for any practical application. Our methods enable scaling full CP to large real-world datasets. We compare our full CP approximation (ACP) to mainstream CP alternatives, and observe that our method is computationally competitive whilst enjoying the statistical predictive power of full CP.