Expanding the AI Evaluation Toolbox with Statistical Models

Benchmarks are widely used to evaluate and compare the performance of artificial intelligence systems. However, some approaches to computing benchmark metrics produce invalid uncertainty estimates or make unrecognized assumptions about the evaluation setting. We leverage statistical modeling to make two contributions to the practice of AI benchmarking. First, we formally distinguish measurements of benchmark accuracy from generalized accuracy (performance on all potential test items similar to those included in the benchmark). Then, in a simulated setting and with large-scale evaluation of 22 API-access frontier large language models on 3 popular benchmarks, we show how analysis via generalized linear mixed model can produce correct estimates of generalized accuracy while more efficiently quantifying uncertainty compared to existing regression-free approaches. We also show how this approach can equip evaluators with important context on evaluation results, including variance decomposition and item difficulty estimates that illuminate important aspects of LLM performance and benchmark construction.

One common way to measure the performance or behavior of large language models (LLMs) or other artificial intelligence (AI) systems is to conduct benchmark evaluations, tests for AI systems involving standardized questions or tasks. One challenge of interpreting these tests is that AI evaluators don’t always quantify how uncertain results are, and may rely on hidden or unstated mathematical assumptions when they report accuracy and other statistics about benchmark performance. Our paper suggests an explicit statistical model of the benchmark evaluation setting that helps evaluators clarify exactly what they are trying to measure. We also compare two different methods for how to analyze benchmark results: a simpler method and a more complex method that uses a “generalized linear mixed model” (GLMM), an elaboration on linear regression. We show how using GLMMs can help evaluators better describe AI performance and benchmark characteristics compared to simpler methods, though GLLMs rely on more assumptions. Future work could build on this approach and elaborate on the tradeoffs with other analysis methods. Overall, our paper demonstrates how using explicit statistical modeling can help increase understanding of and confidence in benchmark results, benefitting future AI developers, adopters, and decision-makers.