Multi‐split conformal prediction via Cauchy aggregation

Abstract

Conformal inference is a popular tool for constructing prediction intervals (PIs). Due to the consideration of computational burden, one of the most commonly used conformal methods is split conformal, which generally suffers from introducing extra randomness and reducing the effectiveness of training models. A natural remedy is to use multiple splits; however, it is still challenging to obtain valid PIs because of the dependence across the splits. In this paper, we propose a simple yet efficient multi‐split conformal prediction method via adapting Cauchy aggregation, which is a powerful tool for combining ‐values with arbitrary correlation structures. Under two different kinds of general conditions, we show that our method is able to yield asymptotically‐exact PIs. Numerical results show that the resulting intervals outperform existing methods in many settings, especially when the stability condition of regression modelling does not satisfy well.

A confidence machine for sparse high‐order interaction model

“…Other works in this direction are Bonferroni-type aggregation (Lei & Wasserman, 2014;Solari & Djordjilovi c, 2022), Cauchy-type aggregation (Wu et al, 2023), out-of-bag ensemble (Gupta et al, 2022) and resampling techniques (Dunn et al, 2022). However, all these methods either depend on strong stability assumption of the underlying model or overly conservative.…”