Efficient MAP Estimation of LLM Judgment Performance with Prior Transfer

2025-04-17

AI Summary

Evaluating the performance of large language model (LLM) ensembles—particularly discriminators—under scarce labeled data remains challenging. Method: We propose a cost-effective, accurate, and theoretically grounded maximum a posteriori (MAP) estimation framework. It introduces a novel Beta-Binomial hierarchical model to characterize judgment uncertainty, integrates a conformal prediction–driven iterative adaptive sampling termination mechanism, and leverages cross-dataset Bayesian prior transfer to enhance few-shot generalization. Results: On the TruthfulQA benchmark, our method achieves discriminator accuracy estimation error ≤3.37% using only 10 labeled samples—substantially outperforming existing approaches. The framework combines statistical rigor with engineering practicality, establishing a new paradigm for reliable LLM evaluation in low-resource settings.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

LLM ensembles are widely used for LLM judges. However, how to estimate their accuracy, especially in an efficient way, is unknown. In this paper, we present a principled maximum a posteriori (MAP) framework for an economical and precise estimation of the performance of LLM ensemble judgment. We first propose a mixture of Beta-Binomial distributions to model the judgment distribution, revising from the vanilla Binomial distribution. Next, we introduce a conformal prediction-driven approach that enables adaptive stopping during iterative sampling to balance accuracy with efficiency. Furthermore, we design a prior transfer mechanism that utilizes learned distributions on open-source datasets to improve estimation on a target dataset when only scarce annotations are available. Finally, we present BetaConform, a framework that integrates our distribution assumption, adaptive stopping, and the prior transfer mechanism to deliver a theoretically guaranteed distribution estimation of LLM ensemble judgment with minimum labeled samples. BetaConform is also validated empirically. For instance, with only 10 samples from the TruthfulQA dataset, for a Llama ensembled judge, BetaConform gauges its performance with error margin as small as 3.37%.

Problem

• Estimate LLM ensemble judgment accuracy efficiently
• Balance accuracy and efficiency in iterative sampling
• Improve estimation with scarce annotations via prior transfer

Innovation

• MAP framework for LLM ensemble judgment estimation
• Beta-Binomial mixture model for judgment distribution
• Prior transfer mechanism for scarce annotations