Adaptive inference with random ellipsoids through Conformal Conditional Linear Expectation

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.