Uncertainty Regions for Multi-Target Regression via Input- Dependent Conformal Calibration

TMLR Paper6756 Authors

Abstract: We consider the problem of provable and effective uncertainty quantification (UQ) for multi-target regression tasks where we need to predict multiple related target variables. This is important in many safety-critical applications in domains including healthcare, engineering, and finance. Conformal prediction (CP) is a promising framework for calibrating predictive models for UQ with guaranteed finite sample coverage. There is relatively less work on multi-target CP compared to single-target CP, and existing methods tend to produce large prediction regions that are not useful in real-world applications. This paper proposes a novel approach referred to as {\em Adaptive Prediction Regions (APR)} to produce provably smaller prediction regions by exploiting heterogeneity in the input data. APR is inspired by the principle behind localized CP for single-target \cite{guan2023localized} and extends it to multi-target settings. The key idea behind APR is to perform adaptive calibration by assigning differential weights to multi-dimensional calibration examples based on their similarity to a test input. We theoretically analyze APR and show that it (a) achieves finite-sample coverage guarantees; and (b) constructs smaller prediction regions. Our experiments on diverse real-world datasets with various numbers of targets show that APR outperforms existing methods by producing significantly smaller prediction regions (achieving up to 85.51\% reduction in region area) over state-of-the-art multi-target CP methods.

Submission Type: Long submission (more than 12 pages of main content)

Assigned Action Editor: ~Michele_Caprio1

Submission Number: 6756