CONTRA: Conformal Prediction Region via Normalizing Flow Transformation

TL;DR

CONTRA introduces a novel method using normalizing flows to create reliable, high-dimensional prediction regions with guaranteed coverage, outperforming traditional conformal prediction techniques.

Contribution

It proposes a new approach leveraging normalizing flows for conformal prediction, enabling accurate multi-dimensional prediction regions with guaranteed coverage.

Findings

CONTRA maintains coverage guarantees across datasets.

It produces sharper, more accurate prediction regions than traditional methods.

The extension improves existing models with reliable prediction regions.

Abstract

Density estimation and reliable prediction regions for outputs are crucial in supervised and unsupervised learning. While conformal prediction effectively generates coverage-guaranteed regions, it struggles with multi-dimensional outputs due to reliance on one-dimensional nonconformity scores. To address this, we introduce CONTRA: CONformal prediction region via normalizing flow TRAnsformation. CONTRA utilizes the latent spaces of normalizing flows to define nonconformity scores based on distances from the center. This allows for the mapping of high-density regions in latent space to sharp prediction regions in the output space, surpassing traditional hyperrectangular or elliptical conformal regions. Further, for scenarios where other predictive models are favored over flow-based models, we extend CONTRA to enhance any such model with a reliable prediction region by training a simple normalizing flow on the residuals. We demonstrate that both CONTRA and its extension maintain guaranteed coverage probability and outperform existing methods in generating accurate prediction regions across various datasets. We conclude that CONTRA is an effective tool for (conditional) density estimation, addressing the under-explored challenge of delivering multi-dimensional prediction regions.