Sparse Conformal Predictors

TL;DR

This paper introduces a new method combining conformal prediction with LASSO for constructing sparse, reliable prediction intervals in high-dimensional linear models, ensuring high coverage with small confidence sets.

Contribution

It proposes a novel conformal prediction approach integrated with LASSO for sparse multivariate linear models, including a data-driven penalty selection procedure.

Findings

Confidence sets have coverage ≥ 1 - ε.

Confidence set length is small in numerical experiments.

Method effectively identifies relevant covariates in simulations.

Abstract

Conformal predictors, introduced by Vovk et al. (2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. In the present paper, we propose a novel method for constructing prediction intervals for the response variable in multivariate linear models. The main emphasis is on sparse linear models, where only few of the covariates have significant influence on the response variable even if their number is very large. Our approach is based on combining the principle of conformal prediction with the $\ell_1$ penalized least squares estimator (LASSO). The resulting confidence set depends on a parameter $\epsilon>0$ and has a coverage probability larger than or equal to $1-\epsilon$. The numerical experiments reported in the paper show that the length of the confidence set is small. Furthermore, as a by-product of the proposed approach, we provide a data-driven procedure for choosing the LASSO penalty. The selection power of the method is illustrated on simulated data.