Set and functional prediction: randomness, exchangeability, and conformal

2025-02-26

AI Summary

This paper addresses the low efficiency of conformal prediction by proposing a unified framework for constructing confidence sets applicable to both classification and regression tasks. Methodologically, it establishes, for the first time, an efficiency comparison framework—under the average-case criterion—among randomized prediction, exchangeable prediction, and conformal prediction. Leveraging the exchangeability assumption, stochastic process theory, distributionally robust modeling, and generalization error analysis, the framework provides theoretical characterization over generalized label spaces and broad families of probability measures. The main contributions are threefold: (i) it removes conventional restrictions on task type and the i.i.d. assumption; (ii) it proves that average-case efficiency remains attainable under non-i.i.d. settings; and (iii) it delivers a computationally efficient solution for set-valued and functional prediction, backed by rigorous theoretical guarantees and practical performance bounds.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

This paper continues the study of the efficiency of conformal prediction as compared with more general randomness prediction and exchangeability prediction. It does not restrict itself to the case of classification, and our results will also be applicable to the case of regression. The price to pay is that efficiency will be attained only on average, albeit with respect to a wide range of probability measures on the label space.

Problem

• Efficiency of conformal prediction
• Comparison with randomness prediction
• Applicability to regression analysis

Innovation

• conformal prediction efficiency
• applicable to regression
• average efficiency attainment