Multivariate Conformal Selection
Tian Bai, Yue Zhao, Xiang Yu, Archer Y. Yang
Abstract
Selecting high-quality candidates from large datasets is critical in applications such as drug discovery, precision medicine, and alignment of large language models (LLMs). While Conformal Selection (CS) provides rigorous uncertainty quantification, it is limited to univariate responses and scalar criteria. To address this, we propose Multivariate Conformal Selection (mCS), a generalization of CS designed for multivariate response settings. Our method introduces regional monotonicity and employs multivariate nonconformity scores to construct conformal $p$-values, enabling finite-sample False Discovery Rate (FDR) control. We present two variants: $\texttt{mCS-dist}$, using distance-based scores, and $\texttt{mCS-learn}$, which learns optimal scores via differentiable optimization. Experiments on simulated and real-world datasets demonstrate that mCS significantly improves selection power while maintaining FDR control, establishing it as a robust framework for multivariate selection tasks.
BibTeX
@inproceedings{
bai2025multivariate,
title={Multivariate Conformal Selection},
author={Tian Bai and Yue Zhao and Xiang Yu and Archer Y. Yang},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=g2tr7nA4pS}
}