Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks

TL;DR

This paper introduces zono-conformal prediction, a novel, computationally efficient method for uncertainty quantification in regression and classification that constructs prediction zonotopes with guaranteed coverage, outperforming traditional interval-based approaches.

Contribution

The paper presents zono-conformal prediction, a new approach that directly incorporates zonotopic uncertainty sets into models, enabling data-efficient, coverage-guaranteed predictions for neural networks.

Findings

Less conservative than interval models and standard conformal methods

Achieves similar coverage with improved efficiency

Applicable to both regression and classification tasks

Abstract

Conformal prediction is a popular uncertainty quantification method that augments a base predictor to return sets of predictions with statistically valid coverage guarantees. However, current methods are often computationally expensive and data-intensive, as they require constructing an uncertainty model before calibration. Moreover, existing approaches typically represent the prediction sets with intervals, which limits their ability to capture dependencies in multi-dimensional outputs. We address these limitations by introducing zono-conformal prediction, a novel approach inspired by interval predictor models and reachset-conformant identification that constructs prediction zonotopes with assured coverage. By placing zonotopic uncertainty sets directly into the model of the base predictor, zono-conformal predictors can be identified via a single, data-efficient linear program. While we can apply zono-conformal prediction to arbitrary nonlinear base predictors, we focus on feed-forward neural networks in this work. Aside from regression tasks, we also construct optimal zono-conformal predictors in classification settings where the output of an uncertain predictor is a set of possible classes. We provide probabilistic coverage guarantees and present methods for detecting outliers in the identification data. In extensive numerical experiments, we show that zono-conformal predictors are less conservative than interval predictor models and standard conformal prediction methods, while achieving a similar coverage over the test data.