提出最小体积多元回归预测集，兼顾准确与效率。
Minimum Volume Conformal Sets for Multivariate Regression
- 设计新损失函数，直接优化预测集体积
- 在真实数据集上实现高覆盖率且体积更小
- 适合需要可靠预测范围的工程应用
置信预测提供了一种具有有限样本有效性原则的预测集构建框架。尽管大部分研究集中于单变量响应变量，现有多元方法要么施加严格的几何假设，要么依赖灵活但计算成本高昂的方法，且不显式优化预测集体积。我们提出一种基于新型损失函数的优化驱动框架，直接学习最小体积覆盖集，同时确保有效覆盖率。该公式自然引出一种新的非一致性评分，可适应残差分布和协变量。我们的方法在任意范数球定义的预测集上进行优化，包括单范数和多范数形式。此外，通过联合优化预测模型和预测不确定性，获得紧致、信息丰富且计算高效的预测集，在真实数据集实验中得到验证。
原文摘要 · Abstract (English)
Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid geometric assumptions or rely on flexible but computationally expensive approaches that do not explicitly optimize prediction set volume. We propose an optimization-driven framework based on a novel loss function that directly learns minimum-volume covering sets while ensuring valid coverage. This formulation naturally induces a new nonconformity score for conformal prediction, which adapts to the residual distribution and covariates. Our approach optimizes over prediction sets defined by arbitrary norm balls, including single and multi-norm formulations. Additionally, by jointly optimizing both the predictive model and predictive uncertainty, we obtain prediction sets that are tight, informative, and computationally efficient, as demonstrated in our experiments on real-world datasets.
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