Interpretable Multivariate Conformal Prediction with Fast Transductive Standardization

TL;DR

This paper introduces a fast, interpretable conformal prediction method for multivariate outputs that provides tight, valid prediction intervals without complex modeling of output dependencies, suitable for limited data scenarios.

Contribution

It presents a novel coordinate-wise standardization technique for multivariate conformal prediction that is computationally efficient and does not require modeling cross-output dependencies.

Findings

Produces tighter prediction intervals than existing methods.

Guarantees finite-sample simultaneous coverage.

Works efficiently with limited data.

Abstract

We propose a conformal prediction method for constructing tight simultaneous prediction intervals for multiple, potentially related, numerical outputs given a single input. This method can be combined with any multi-target regression model and guarantees finite-sample coverage. It is computationally efficient and yields informative prediction intervals even with limited data. The core idea is a novel \emph{coordinate-wise} standardization procedure that makes residuals across output dimensions directly comparable, estimating suitable scaling parameters using the calibration data themselves. This does not require modeling of cross-output dependence nor auxiliary sample splitting. Implementing this idea requires overcoming technical challenges associated with transductive or full conformal prediction. Experiments on simulated and real data demonstrate this method can produce tighter prediction intervals than existing baselines while maintaining valid simultaneous coverage.