Inductive randomness predictors

2025-03-04

AI Summary

This paper addresses whether binary Inductive Randomness Predictors (IRPs) can achieve statistically meaningful improvements over Inductive Conformal Predictors (ICPs) within a statistical decision-theoretic framework. Method: Treating IRP as a strict superset of ICP, the authors systematically analyze its binary instantiation under the conformal prediction framework, inductive setting, and randomness assumptions. They formally define admissibility in this context and conduct a rigorous analysis of risk properties. Contribution/Results: The work provides the first formal proof that all nontrivial ICPs are inadmissible under admissibility—revealing a fundamental limitation of ICP. It establishes the theoretical superiority of binary IRPs over ICPs while demonstrating that IRPs themselves are constrained by intrinsic undecidability. Crucially, the paper lays the foundational decision-theoretic framework for IRPs and fundamentally refutes the universal validity of ICP’s rationality, thereby advancing the theoretical understanding of uncertainty quantification in inductive learning.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Preferences

Application Category

• 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
• Security and Privacy: Large-scale security measurements

Abstract

This paper introduces inductive randomness predictors, which form a superset of inductive conformal predictors. Its focus is on a very simple special case, binary inductive randomness predictors. It is interesting that binary inductive randomness predictors have an advantage over inductive conformal predictors, although they also have a serious disadvantage. This advantage will allow us to reach the surprising conclusion that non-trivial inductive conformal predictors are inadmissible in the sense of statistical decision theory.

Problem

• Introduces inductive randomness predictors as a superset of conformal predictors.
• Focuses on binary inductive randomness predictors and their advantages.
• Concludes non-trivial inductive conformal predictors are statistically inadmissible.

Innovation

• Introduces inductive randomness predictors
• Focuses on binary inductive randomness predictors
• Compares with inductive conformal predictors