Improving conformalized quantile regression through cluster-based feature relevance

Abstract

Conformalized quantile regression, a cutting-edge and model-agnostic algorithm, has emerged as a recent innovation to generate valid prediction intervals on finite samples while addressing heteroscedasticity. It starts by employing quantile regression to estimate conditional quantiles. Subsequently, these estimated conditional quantiles undergo a rectification process using conformal prediction. Under the assumption of exchangeability, a slightly weaker form of independent and identically distributed (i.i.d.) data, the resulting prediction intervals are valid in finite samples. However, a drawback of the proposed conformalization step is identified: it lacks the capacity to adapt to heteroscedasticity due to its independence from the input. To overcome this limitation, we propose an improvement that involves partitioning the covariates space into clusters, assigning higher weights to features with greater predictive power. Following that, within each cluster, a conformal step is applied, leveraging a rectification that is reliant on the input cluster-wise.To demonstrate the superiority of our improved version over the classic version of conformalized quantile regression, we conducted a comprehensive comparison of their respective prediction intervals using synthetic data.