Reliable Statistical Guarantees for Conformal Predictors with Small Datasets

TL;DR

This paper introduces a new statistical guarantee for conformal predictors that remains reliable with small datasets, improving uncertainty quantification in surrogate models for safety-critical applications.

Contribution

It proposes a probabilistic coverage guarantee for conformal predictors that is effective even with limited calibration data, bridging the gap in existing methods.

Findings

The new guarantee converges to standard CP with large datasets.

It provides meaningful coverage information for small calibration sets.

Validated through multiple examples and implemented in open-source software.

Abstract

Surrogate models (including deep neural networks and other machine learning algorithms in supervised learning) are capable of approximating arbitrarily complex, high-dimensional input-output problems in science and engineering, but require a thorough data-agnostic uncertainty quantification analysis before these can be deployed for any safety-critical application. The standard approach for data-agnostic uncertainty quantification is to use conformal prediction (CP), a well-established framework to build uncertainty models with proven statistical guarantees that do not assume any shape for the error distribution of the surrogate model. However, since the classic statistical guarantee offered by CP is given in terms of bounds for the marginal coverage, for small calibration set sizes (which are frequent in realistic surrogate modelling that aims to quantify error at different regions), the potentially strong dispersion of the coverage distribution around its average negatively impacts the relevance of the uncertainty model's statistical guarantee, often obtaining coverages below the expected value, resulting in a less applicable framework. After providing a gentle presentation of uncertainty quantification for surrogate models for machine learning practitioners, in this paper we bridge the gap by proposing a new statistical guarantee that offers probabilistic information for the coverage of a single conformal predictor. We show that the proposed framework converges to the standard solution offered by CP for large calibration set sizes and, unlike the classic guarantee, still offers relevant information about the coverage of a conformal predictor for small data sizes. We validate the methodology in a suite of examples, and implement an open access software solution that can be used alongside common conformal prediction libraries to obtain uncertainty models that fulfil the new guarantee.