Conditional Flow Matching for Conformal Regression

Rui Luo, Jie Bao, nicolo colombo, Chuangyin Dang, Suqun Cao, XIAOFENG SONG

Keywords: Conformal prediction, conformal regression, conditional flow matching

Abstract: This paper introduces Conditional flow Matching for conformal Regression (CMR), a novel framework that synergizes simulation-free conditional flow matching with conformal prediction to generate reliable and efficient prediction intervals. Unlike traditional methods that rely on quantile regression or fixed histograms, CMR leverages Continuous Normalizing Flows (CNFs) trained via Conditional Flow Matching (CFM) to accurately model complex, multimodal conditional distributions. To ensure finite-sample coverage guarantees, we introduce a novel nonconformity score defined as the minimum number of generated samples required for the shortest interval to encompass the true outcome. This mechanism allows CMR to dynamically adjust interval widths based on the learned probability density. Extensive experiments on simulated and real-world datasets demonstrate that CMR consistently produces narrower prediction intervals while maintaining the required marginal coverage and achieving superior tail coverage compared to state-of-the-art methods.

Primary Area: interpretability and explainable AI

Submission Number: 3141