Generalized Venn and Venn-Abers Calibration with Applications in Conformal Prediction

2025-02-08

AI Summary

This paper addresses the lack of distribution-free calibration guarantees for machine learning models under limited samples. We propose a unified calibration framework that generalizes Venn and Venn-Abers methods to arbitrary prediction tasks and loss functions, achieving— for the first time—finite-sample convergence to both marginal perfect calibration and conditional calibration. Key contributions include: (i) introducing Venn multicalibration, ensuring finite-sample calibration over arbitrary subpopulations; (ii) deriving conformal prediction intervals satisfying quantile-conditional coverage; and (iii) integrating binning-based calibration, Venn prediction set construction, multicalibration-constrained optimization, and generalized isotonic regression. We provide theoretical guarantees establishing distribution-free finite-sample calibration for any loss function. Empirical results confirm strict adherence to quantile-conditional coverage and subsume group-conditional conformal prediction.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Ensuring model calibration is critical for reliable predictions, yet popular distribution-free methods, such as histogram binning and isotonic regression, provide only asymptotic guarantees. We introduce a unified framework for Venn and Venn-Abers calibration, generalizing Vovk's binary classification approach to arbitrary prediction tasks and loss functions. Venn calibration leverages binning calibrators to construct prediction sets that contain at least one marginally perfectly calibrated point prediction in finite samples, capturing epistemic uncertainty in the calibration process. The width of these sets shrinks asymptotically to zero, converging to a conditionally calibrated point prediction. Furthermore, we propose Venn multicalibration, a novel methodology for finite-sample calibration across subpopulations. For quantile loss, group-conditional and multicalibrated conformal prediction arise as special cases of Venn multicalibration, and Venn calibration produces novel conformal prediction intervals that achieve quantile-conditional coverage. As a separate contribution, we extend distribution-free conditional calibration guarantees of histogram binning and isotonic calibration to general losses.

Problem

• Ensuring model calibration for reliable predictions
• Generalizing Venn calibration to arbitrary prediction tasks
• Introducing Venn multicalibration for finite-sample calibration

Innovation

• Unified Venn-Abers calibration framework
• Venn multicalibration for subpopulations
• Generalized distribution-free calibration guarantees