标题： 多元保形选择 显示英文标题

标题： Multivariate Conformal Selection

摘要： 从大型数据集中选择高质量候选者在药物发现、精准医疗和大规模语言模型（LLM）的对齐等应用中至关重要。虽然一致性选择（CS）提供了严格的不确定性量化，但它仅限于单变量响应和标量标准。为了解决这个问题，我们提出了多变量一致性选择（mCS），这是为多变量响应设置设计的CS的一般化。我们的方法引入了区域单调性，并使用多变量非一致性分数来构造一致性p值，从而实现有限样本下的假发现率（FDR）控制。我们介绍了两种变体：mCS-dist，使用基于距离的分数，以及mCS-learn，通过可微优化学习最优分数。在模拟和真实数据集上的实验表明，mCS显著提高了选择能力，同时保持了FDR控制，确立了它作为多变量选择任务的强大框架。 显示英文摘要

摘要： 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.