Efficient Evaluation of LLM Performance with Statistical Guarantees

Large Language Models (LLMs) exhibit systematic biases across demographic groups. Auditing is proposed as an accountability tool for black-box LLM applications, but suffers from resource-intensive query access. We conceptualise auditing as uncertainty estimation over a target fairness metric and introduce BAFA, the Bounded Active Fairness Auditor for query-efficient auditing of black-box LLMs. BAFA maintains a version space of surrogate models consistent with queried scores and computes uncertainty intervals for fairness metrics (e.g., $Δ$ AUC) via constrained empirical risk minimisation. Active query selection narrows these intervals to reduce estimation error. We evaluate BAFA on two standard fairness dataset case studies: CivilComments and Bias-in-Bios, comparing against stratified sampling, power sampling, and ablations. BAFA achieves target error thresholds with up to 40$\times$ fewer queries than stratified sampling (e.g., 144 vs 5,956 queries at $\varepsilon=0.02$ for CivilComments) for tight thresholds, demonstrates substantially better performance over time, and shows lower variance across runs. These results suggest that active sampling can reduce resources needed for independent fairness auditing with LLMs, supporting continuous model evaluations.

We study the problem of sequentially evaluating a new large language model (LLM) on a fixed question set using historical performance data from prior LLMs. Our goal is to construct a confidence sequence (CS) for the model's capability on this question set and to design active querying rules that shrink the CS width as quickly as possible. For CS construction, we invert a family of test supermartingales and focus on two representative approaches: a reverse information projection (RIPr)-based approach and a testing-by-betting-based approach. We first study these approaches under an oracle setting, and demonstrate the oracle optimality of the RIPr-based construction. We then propose a growth-oriented querying rule that aims to maximize the worst-case one-step expected log-increment over the endpoints of the current CS. In practice, we build these test supermartingales and the querying rule on predictions of question-level correctness learned from historical data. We then analyze the shrinkage behavior of the resulting CSs and identify two key factors that slow the shrinkage rate of CSs: accumulated prediction mismatch and the spikiness of the querying distribution. Finally, motivated by this analysis, we propose several mixture querying rules that combine growth-oriented querying, prediction refinement, and uniform exploration, trying to mitigate the effects that slow the shrinkage rate. We provide experiments comparing different querying rules for the RIPr-based and testing-by-betting-based CSs across several synthetic testing datasets. Interestingly, we observe that the simplest querying rule, uniform sampling, can sometimes outperform more adaptive querying rules for both methods.

Efficient benchmarking techniques aim to lower the computational cost of evaluating LLMs by predicting full benchmark scores using only a subset of a benchmark's questions. By reframing this problem as an instance of multiple regression with feature selection, we find that existing efficient benchmarking methods can be greatly improved by simply using kernel ridge regression at the prediction stage. Additionally, using an information-theoretic feature-selection algorithm called minimum redundancy maximum relevance (mRMR), we can further improve upon these methods by selecting question subsets that will be maximally useful for prediction. Except in very data-poor settings, these approaches consistently achieve smaller prediction errors (in both MAE and RMSE), and greater ranking correlation between predicted and true scores (in both Spearman $ρ$ and Kendall $τ$) across a range of benchmarks using both binary and continuous metrics. Furthermore, mRMR subsampling is much faster than competitor methods (which often involve fitting probabilistic models or running clustering algorithms), and is more likely to select the same questions under different random seeds or training data splits. Tutorial code can be found at https://github.com/sambowyer/mrmr_eval .