Multivariate Conformal Selection
This work addresses a critical need in applications like drug discovery and LLM alignment by extending rigorous uncertainty quantification to multivariate settings, representing an incremental advancement over univariate methods.
The paper tackles the problem of selecting high-quality candidates from large datasets with multivariate responses, where existing conformal selection methods are limited to univariate settings, and proposes Multivariate Conformal Selection (mCS) to achieve finite-sample False Discovery Rate (FDR) control while significantly improving selection power in experiments.
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 issue, 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: mCS-dist, using distance-based scores, and 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.