Robust Optimization for Inference on Machine Learning Generated Variables

Abstract

Leveraging supervised machine learning (SML) algorithms to operationalize constructs from unstructured data like text or images is becoming common in practice and research. As a result, variables generated through SML are used in regression models to make inferences and test theories. However, variables produced by SML will have measurement errors compared to the underlying construct. We propose using robust optimization to reduce the negative impact of these errors and produce less biased coefficient estimates while conducting more accurate hypothesis testing. To extend the burgeoning literature on this issue, our proposed method focuses on the generalized research setting where a flexible number of dependent and independent variables are measured by SML algorithms. We combine recent robust optimization techniques to fit a linear regression model in the presence of uncertain measurement error. We theoretically demonstrate the consistency and efficiency of the robust approach. Through simulations, we demonstrate the effectiveness of our approach.