Moran Guo

Yiqun T Chen, Sizhu Lu, Sijia Li et al.

Large language models (LLMs) are increasingly used as automatic evaluators of generative AI outputs, a paradigm often referred to as "LLM-as-a-judge." In practice, LLM judges are imperfect predictions for the underlying truth and can exhibit systematic, non-random errors. Two main approaches have recently been proposed to address this issue: (i) direct measurementerror correction based on misclassification models such as Rogan-Gladen-style estimators, and (ii) surrogate-outcome approaches such as prediction-powered inference (PPI), which correct bias by calibrating prediction residuals on a small set of gold-standard human labels. In this paper, we systematically study the performance of these two approaches for estimating mean parameters (e.g., average benchmark scores or pairwise win rates). Leveraging tools from semiparametric efficiency theory, we unify the two classes of estimators by deriving explicit forms of efficient influence function (EIF)-based efficient estimators and characterize conditions under which PPI-style estimators attain strictly smaller asymptotic variance than measurement-error corrections. We verify our theoretical results in simulations and demonstrate the methods on real-data examples. We provide an implementation of the benchmarked methods and comparison utilities at https://github.com/yiqunchen/debias-llm-as-a-judge.

Yiqun T. Chen, Moran Guo, Shengy Li

Modern studies increasingly leverage outcomes predicted by machine learning and artificial intelligence (AI/ML) models, and recent work, such as prediction-powered inference (PPI), has developed valid downstream statistical inference procedures. However, classical power and sample size formulas do not readily account for these predictions. In this work, we tackle a simple yet practical question: given a new AI/ML model with high predictive power, how many labeled samples are needed to achieve a desired level of statistical power? We derive closed-form power formulas by characterizing the asymptotic variance of the PPI estimator and applying Wald test inversion to obtain the required labeled sample size. Our results cover widely used settings including two-sample comparisons and risk measures in 2x2 tables. We find that a useful rule of thumb is that the reduction in required labeled samples relative to classical designs scales roughly with the R2 between the predictions and the ground truth. Our analytical formulas are validated using Monte Carlo simulations, and we illustrate the framework in three contemporary biomedical applications spanning single-cell transcriptomics, clinical blood pressure measurement, and dermoscopy imaging. We provide our software as an R package and online calculators at https://github.com/yiqunchen/pppower.