Asymmetric conformal prediction with penalized kernel sum-of-squares

TL;DR

This paper introduces an asymmetric conformal prediction method that adapts to skewed noise distributions, improving prediction intervals by balancing symmetry and asymmetry based on data characteristics.

Contribution

It proposes a new adaptive, asymmetric conformal prediction framework using kernel sum-of-squares and a penalty mechanism to handle skewed residuals.

Findings

The method effectively adapts from symmetric to asymmetric intervals.

It improves prediction interval accuracy in biased or small sample scenarios.

A data-driven penalty selection enhances model flexibility.

Abstract

Conformal prediction (CP) is a distribution-free method to construct reliable prediction intervals that has gained significant attention in recent years. Despite its success and various proposed extensions, a significant practical feature which has been overlooked in previous research is the potential skewed nature of the noise, or of the residuals when the predictive model exhibits bias. In this work, we leverage recent developments in CP to propose a new asymmetric procedure that bridges the gap between skewed and non-skewed noise distributions, while still maintaining adaptivity of the prediction intervals. We introduce a new statistical learning problem to construct adaptive and asymmetric prediction bands, with a unique feature based on a penalty which promotes symmetry: when its intensity varies, the intervals smoothly change from symmetric to asymmetric ones. This learning problem is based on reproducing kernel Hilbert spaces and the recently introduced kernel sum-of-squares framework. First, we establish representer theorems to make our problem tractable in practice, and derive dual formulations which are essential for scalability to larger datasets. Second, the intensity of the penalty is chosen using a novel data-driven method which automatically identifies the symmetric nature of the noise. We show that consenting to some asymmetry can let the learned prediction bands better adapt to small sample regimes or biased predictive models.