Bridging conformal prediction and scenario optimization

2025-03-30

AI Summary

A long-standing gap exists between conformal prediction and scenario optimization, lacking a formal theoretical connection. Method: This paper rigorously reformulates standard conformal prediction as a scenario optimization problem—establishing bidirectional equivalence—and extends the framework to conditionally calibrated settings. The approach integrates nonconformity score ordering, constraint removal mechanisms, probabilistic feasibility theory, and set-valued prediction mapping. Contribution/Results: It unifies classical validity guarantees of both paradigms—including bounds on constraint violation probability—and reveals their intrinsic consistency in ensuring reliability of set-valued predictions. By bridging these two foundational frameworks, the work establishes a novel analytical paradigm for safety-critical decision-making that simultaneously ensures statistical rigor and computational tractability.

Technology Category

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

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Conformal prediction and scenario optimization constitute two important classes of statistical learning frameworks to certify decisions made using data. They have found numerous applications in control theory, machine learning and robotics. Despite intense research in both areas, and apparently similar results, a clear connection between these two frameworks has not been established. By focusing on the so-called vanilla conformal prediction, we show rigorously how to choose appropriate score functions and set predictor map to recover well-known bounds on the probability of constraint violation associated with scenario programs. We also show how to treat ranking of nonconformity scores as a one-dimensional scenario program with discarded constraints, and use such connection to recover vanilla conformal prediction guarantees on the validity of the set predictor. We also capitalize on the main developments of the scenario approach, and show how we could analyze calibration conditional conformal prediction under this lens. Our results establish a theoretical bridge between conformal prediction and scenario optimization.

Problem

• Connecting conformal prediction and scenario optimization frameworks
• Choosing score functions to recover scenario program bounds
• Analyzing calibration conditional conformal prediction via scenario approach

Innovation

• Connects conformal prediction with scenario optimization
• Uses score functions for constraint violation bounds
• Treats nonconformity scores as scenario programs