Generative Conformal Prediction with Vectorized Non-Conformity Scores

TL;DR

This paper introduces a generative conformal prediction method that uses vectorized non-conformity scores to create adaptive, less conservative uncertainty sets, improving uncertainty quantification in multi-dimensional models.

Contribution

It proposes a novel generative conformal prediction framework with vectorized scores, enabling adaptive and efficient uncertainty sets with theoretical validity guarantees.

Findings

Outperforms existing methods on synthetic datasets.

Provides tighter, more adaptive uncertainty sets.

Demonstrates strong empirical validity on real-world data.

Abstract

Conformal prediction (CP) provides model-agnostic uncertainty quantification with guaranteed coverage, but conventional methods often produce overly conservative uncertainty sets, especially in multi-dimensional settings. This limitation arises from simplistic non-conformity scores that rely solely on prediction error, failing to capture the prediction error distribution's complexity. To address this, we propose a generative conformal prediction framework with vectorized non-conformity scores, leveraging a generative model to sample multiple predictions from the fitted data distribution. By computing non-conformity scores across these samples and estimating empirical quantiles at different density levels, we construct adaptive uncertainty sets using density-ranked uncertainty balls. This approach enables more precise uncertainty allocation -- yielding larger prediction sets in high-confidence regions and smaller or excluded sets in low-confidence regions -- enhancing both flexibility and efficiency. We establish theoretical guarantees for statistical validity and demonstrate through extensive numerical experiments that our method outperforms state-of-the-art techniques on synthetic and real-world datasets.