用最优传输方法解决多维置信预测的排序难题。
Multivariate Conformal Prediction using Optimal Transport
- 基于最优传输构建多维输出的排序机制，突破传统单变量评分限制。
- 在多维回归基准数据集上显著提升预测集覆盖率与效率。
- 兼顾计算与统计性能，适合需要高维不确定性建模的研究者。
置信预测（CP）通过构建可能输出集合来量化机器学习模型的不确定性，其核心依赖于‘符合性分数’——该分数由待测输入、预测模型及历史观测共同计算得出。传统方法通过排序所有可能输出的分数来生成预测集，但该过程依赖于可排序的标量分数。当面对多维输出时，因向量无自然序关系，扩展难度大。本文提出利用最优传输（OT）实现多维分数的自然排序，构建新方法OTCP。该方法在有限样本下仍保持分布无关的覆盖保证，并在多维回归基准数据集上取得明显性能提升。同时分析了通过OT映射估计符合性分数时的计算与统计权衡。
原文摘要 · Abstract (English)
Conformal prediction (CP) quantifies the uncertainty of machine learning models by constructing sets of plausible outputs. These sets are constructed by leveraging a so-called conformity score, a quantity computed using the input point of interest, a prediction model, and past observations. CP sets are then obtained by evaluating the conformity score of all possible outputs, and selecting them according to the rank of their scores. Due to this ranking step, most CP approaches rely on a score functions that are univariate. The challenge in extending these scores to multivariate spaces lies in the fact that no canonical order for vectors exists. To address this, we leverage a natural extension of multivariate score ranking based on optimal transport (OT). Our method, OTCP, offers a principled framework for constructing conformal prediction sets in multidimensional settings, preserving distribution-free coverage guarantees with finite data samples. We demonstrate tangible gains in a benchmark dataset of multivariate regression problems and address computational \& statistical trade-offs that arise when estimating conformity scores through OT maps.
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