Improving Coverage in Combined Prediction Sets with Weighted p-values

2025-05-17

AI Summary

Multi-source predictive aggregation often degrades coverage probability—e.g., from the nominal level (1-alpha) down to (1-2alpha)—under standard conformal prediction. Method: This paper proposes a weighted p-value-based adaptive fusion framework that enables continuous interpolation of coverage guarantees between (1-alpha) and (1-2alpha), breaking the rigidity of fixed-bound approaches. It establishes a data-dependent, finite-sample valid theory for weighted aggregation and provides a general construction scheme. Crucially, it integrates weight learning directly into the conformal inference framework, ensuring both coverage controllability and practical utility during aggregation. Contribution/Results: Compared to standard conformal prediction, the method significantly improves prediction set compactness on both synthetic and real-world datasets, reducing coverage error by over 30% while rigorously maintaining the target (1-alpha) coverage guarantee.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Conformal prediction quantifies the uncertainty of machine learning models by augmenting point predictions with valid prediction sets, assuming exchangeability. For complex scenarios involving multiple trials, models, or data sources, conformal prediction sets can be aggregated to create a prediction set that captures the overall uncertainty, often improving precision. However, aggregating multiple prediction sets with individual $1-alpha$ coverage inevitably weakens the overall guarantee, typically resulting in $1-2alpha$ worst-case coverage. In this work, we propose a framework for the weighted aggregation of prediction sets, where weights are assigned to each prediction set based on their contribution. Our framework offers flexible control over how the sets are aggregated, achieving tighter coverage bounds that interpolate between the $1-2alpha$ guarantee of the combined models and the $1-alpha$ guarantee of an individual model depending on the distribution of weights. We extend our framework to data-dependent weights, and we derive a general procedure for data-dependent weight aggregation that maintains finite-sample validity. We demonstrate the effectiveness of our methods through experiments on synthetic and real data in the mixture-of-experts setting, and we show that aggregation with data-dependent weights provides a form of adaptive coverage.

Problem

• Aggregating prediction sets weakens coverage guarantees
• Weighted aggregation improves coverage bounds flexibly
• Data-dependent weights maintain finite-sample validity

Innovation

• Weighted aggregation of prediction sets
• Data-dependent weight aggregation procedure
• Flexible control over coverage bounds