CONTRA: Conformal Prediction Region via Normalizing Flow Transformation

2026-05-08

AI Summary

This work addresses the limitations of traditional conformal prediction in multivariate settings, where reliance on one-dimensional nonconformity scores often yields overly conservative or imprecise prediction regions. The authors propose a novel approach that leverages the latent structure of normalizing flows to define a nonconformity score based on centered distances in the latent space. This score is then used to model residuals of any base predictor, enabling the construction of high-density, sharp multivariate prediction regions. By moving beyond conventional hyper-rectangular or ellipsoidal shapes, the method achieves significantly improved region accuracy across multiple datasets while rigorously maintaining the desired coverage probability, outperforming existing state-of-the-art techniques.

Abstract

Density estimation and reliable prediction regions for outputs are crucial in supervised and unsupervised learning. While conformal prediction effectively generates coverage-guaranteed regions, it struggles with multi-dimensional outputs due to reliance on one-dimensional nonconformity scores. To address this, we introduce CONTRA: CONformal prediction region via normalizing flow TRAnsformation. CONTRA utilizes the latent spaces of normalizing flows to define nonconformity scores based on distances from the center. This allows for the mapping of high-density regions in latent space to sharp prediction regions in the output space, surpassing traditional hyperrectangular or elliptical conformal regions. Further, for scenarios where other predictive models are favored over flow-based models, we extend CONTRA to enhance any such model with a reliable prediction region by training a simple normalizing flow on the residuals. We demonstrate that both CONTRA and its extension maintain guaranteed coverage probability and outperform existing methods in generating accurate prediction regions across various datasets. We conclude that CONTRA is an effective tool for (conditional) density estimation, addressing the under-explored challenge of delivering multi-dimensional prediction regions.

Problem

• conformal prediction
• multi-dimensional outputs
• prediction regions
• coverage guarantee
• nonconformity scores

Innovation

• Conformal Prediction
• Normalizing Flow
• Multidimensional Prediction Regions
• Nonconformity Score
• Density Estimation