Generative Conformal Prediction with Vectorized Non-Conformity Scores

• URL: http://arxiv.org/abs/2410.13735v2
• Date: Tue, 11 Feb 2025 11:09:52 GMT
• Title: Generative Conformal Prediction with Vectorized Non-Conformity Scores
• Authors: Minxing Zheng, Shixiang Zhu,
• Abstract summary: Conformal prediction provides model-agnostic uncertainty quantification with guaranteed coverage.<n>We propose a generative conformal prediction framework with vectorized non-conformity scores.<n>We construct adaptive uncertainty sets using density-ranked uncertainty balls.
• Score: 6.059745771017814
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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