We propose a new conformity score for conformal prediction, in a general multivariate regression framework. The underlying score function is based on a covariance analysis of the residuals and the input points. We give theoretical guarantees on the prediction set. This set consists in an explicit ellipsoid that has a reduced volume compared to a classic ball. Further, we also study the asymptotic properties of the ellipsoid. Finally, we illustrate the effectiveness of all our results on an in-depth numerical study.

翻译：我们在一般多元回归框架下，为共形预测提出了一种新的适配度评分。该评分函数基于残差与输入点的协方差分析。我们为预测集提供了理论保证。该预测集由一个显式椭球构成，其体积相较于经典球体有所减小。此外，我们还研究了该椭球的渐近性质。最后，我们通过深入的数值研究展示了所有结果的有效性。