QuEst: Enhancing Estimates of Quantile-Based Distributional Measures Using Model Predictions
This work addresses the need for broader quantile-based measures in fields such as economics and medicine, though it is incremental as it extends existing hybrid-inference methods to more metrics.
The paper tackles the limitation of existing hybrid-inference tools that only target means or single quantiles by introducing QuEst, a framework for estimating quantile-based distributional measures using both observed and imputed data, demonstrating its utility in domains like economic modeling and opinion polling.
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.