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The paper addresses the problem of biased prevalence estimation when using imperfect classifiers, including LLMs, under covariate shift. It demonstrates that multicalibration, which enforces calibration conditional on input features, is sufficient for unbiased prevalence estimation, unlike standard calibration methods. Empirical results on employment prevalence estimation across US states and political text classification across countries show that multicalibration significantly reduces bias.
Multicalibration is the key to unbiased prevalence estimation with LLMs under covariate shift, a problem where standard calibration falls short.
Estimating the prevalence of a category in a population using imperfect measurement devices (diagnostic tests, classifiers, or large language models) is fundamental to science, public health, and online trust and safety. Standard approaches correct for known device error rates but assume these rates remain stable across populations. We show this assumption fails under covariate shift and that multicalibration, which enforces calibration conditional on the input features rather than just on average, is sufficient for unbiased prevalence estimation under such shift. Standard calibration and quantification methods fail to provide this guarantee. Our work connects recent theoretical work on fairness to a longstanding measurement problem spanning nearly all academic disciplines. A simulation confirms that standard methods exhibit bias growing with shift magnitude, while a multicalibrated estimator maintains near-zero bias. While we focus the discussion mostly on LLMs, our theoretical results apply to any classification model. Two empirical applications -- estimating employment prevalence across U.S. states using the American Community Survey, and classifying political texts across four countries using an LLM -- demonstrate that multicalibration substantially reduces bias in practice, while highlighting that calibration data should cover the key feature dimensions along which target populations may differ.
