QuEst: Enhancing Estimates of Quantile-Based Distributional Measures Using Model Predictions

TL;DR

QuEst is a new framework that combines observed data with model predictions to accurately estimate a wide range of quantile-based distributional measures, providing reliable confidence intervals for diverse applications.

Contribution

It introduces a general method for hybrid inference of quantile-based measures, extending to multidimensional metrics and reducing variance in estimates.

Findings

Effective in economic modeling, opinion polling, and language model evaluation.

Provides rigorous confidence intervals for various quantile-based measures.

Outperforms existing methods limited to means or single quantiles.

Abstract

As machine learning models grow increasingly competent, their predictions can supplement scarce or expensive data in various important domains. In support of this paradigm, algorithms have emerged to combine a small amount of high-fidelity observed data with a much larger set of imputed model outputs to estimate some quantity of interest. Yet current hybrid-inference tools target only means or single quantiles, limiting their applicability for many critical domains and use cases. We present QuEst, a principled framework to merge observed and imputed data to deliver point estimates and rigorous confidence intervals for a wide family of quantile-based distributional measures. QuEst covers a range of measures, from tail risk (CVaR) to population segments such as quartiles, that are central to fields such as economics, sociology, education, medicine, and more. We extend QuEst to multidimensional metrics, and introduce an additional optimization technique to further reduce variance in this and other hybrid estimators. We demonstrate the utility of our framework through experiments in economic modeling, opinion polling, and language model auto-evaluation.