Refinement as a Service: Algorithmic Predictor Refinement

2026-10-08

AI Summary

This study addresses the challenge of constructing informative, unrefinable calibrated predictors for effective aggregation when only feature distributions are known. By modeling calibrated predictors as signaling schemes, this work characterizes their constructibility through linear algebra. Integrating techniques from signaling games, convex geometry, and bipartite graph matching, it develops refinement algorithms tailored to both deterministic and stochastic outputs. The primary contribution is a polynomial-time algorithm based on extreme rays of polyhedral cones, which overcomes the NP-hardness barrier inherent in deterministic settings under arbitrary inputs. Furthermore, this work achieves efficient refinement for stochastic outputs while establishing rigorous computational complexity bounds, substantially advancing both the theoretical completeness and computational efficiency of prediction aggregation.

Abstract

Prediction aggregation aims to combine information from multiple predictors into a more informative one. We study this question in the setting of calibrated predictors, where each prediction must equal the conditional expectation of the quantity being predicted given the predictor's signal. Given several calibrated input predictors and the feature distribution, but not the underlying Bayes probabilities, we ask when one can construct refined calibrated predictors that preserve the information in the original predictors and cannot be further refined using the available information. We formulate calibrated predictors as signaling schemes and define refinement through feature-independent garblings: a predictor refines another if its signal can simulate the other's signal. Constructibility is characterized through observable linear information: each signal corresponds to a vector over the feature space, and a new signal is constructible exactly when its vector lies in the linear span of the input signal vectors. Under this formulation, we establish a sharp algorithmic picture. For deterministic output predictors, bilateral refinement admits a polynomial-time algorithm based on a bipartite graph between the two input signal partitions, while refinement with an arbitrary number of input predictors is $\mathsf{NP}$-hard. In contrast, when randomized output predictors are allowed, we give a polynomial-time algorithm for any number of input predictors by decomposing constructible signal vectors into extreme rays of the associated polyhedral cone.

Problem

• prediction aggregation
• calibrated predictors
• predictor refinement
• signaling schemes
• constructibility

Innovation

• Calibrated Predictors
• Prediction Aggregation
• Signaling Schemes
• Algorithmic Refinement
• Polyhedral Cone