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

2025-08-14

AI Summary

Existing uncertainty quantification methods for multivariate regression and classification suffer from high computational overhead, strong data dependence, and limited expressiveness of prediction sets, failing to capture dependencies among output variables. This paper proposes Zono-Conformal Prediction—the first integration of zonotopes into the conformal prediction framework—to construct statistically valid, multivariate prediction sets with guaranteed marginal coverage. By formulating uncertainty quantification as a linear program, our method efficiently computes zonotopic prediction sets, supports nonlinear base models, and overcomes the representational limitations of interval-based approaches. For classification, we introduce an optimal strategy for constructing prediction sets that minimize size while preserving coverage. Experiments demonstrate that, under strict adherence to the target coverage level, our method yields significantly more compact and less conservative prediction sets, while exhibiting robust outlier detection capability.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

Conformal prediction is a popular uncertainty quantification method that augments a base predictor with prediction sets 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.

Problem

• Reduces computational cost of uncertainty quantification methods
• Improves multi-dimensional dependency capture in prediction sets
• Enhances data efficiency with linear program-based zonotope construction

Innovation

• Zonotope-based uncertainty quantification for regression and classification
• Data-efficient linear program for constructing prediction zonotopes
• Probabilistic coverage guarantees with outlier detection