A Random Forest Approach with Amplified Bootstrap for Counting Language Minority Groups in the United States

This paper addresses the challenge of estimating language minority populations for compliance with the U.S. Voting Rights Act (VRA). Current methodologies, which rely on frequentist and Bayesian models developed by the U.S. Census Bureau, are benchmarked against a novel machine learning approach. We use a random forest (RF) model that significantly improves population size estimates for language minority groups. Our key contribution is the development of a modified RF objective function, a beta–binomial distribution, which is specifically tailored to the unique structure of the VRA data. This approach leverages the flexibility of the RF framework to accommodate the VRA data in a statistically principled manner. The resulting RF method demonstrates superior performance on several language minority groups compared to the established 2021 Census Bureau models.