Boosted generalized normal distributions: Integrating machine learning with operations knowledge
Ragip Gurlek, Francis de Vericourt, Donald K. K. Lee
TL;DR
This work tackles the gap between point predictions and distributional forecasts in operations by introducing the Boosted Generalized Normal Distribution ($b$GND), which models $Y|X$ with covariate-dependent location $\mu(x)$ and scale $b(x)$ learned via gradient boosting. By fixing the shape parameter $\gamma$ and decoupling the estimation of $\mu(x)$ and $b(x)$, the authors establish statistical consistency and provide a robust estimation algorithm based on sample-splitting. Empirically, $b$GND improves distributional forecasts in a large emergency department dataset, achieving CRPS gains of about $6.1\%$ for wait times and $8.8\%$ for service times relative to a distribution-agnostic benchmark, with downstream improvements in patient satisfaction and mortality reductions. The paper demonstrates the practical value of integrating operations knowledge with ML for distributional forecasting and highlights the approach’s potential applicability across healthcare operations and other domains requiring reliable distributional predictions.
Abstract
Applications of machine learning (ML) techniques to operational settings often face two challenges: i) ML methods mostly provide point predictions whereas many operational problems require distributional information; and ii) They typically do not incorporate the extensive body of knowledge in the operations literature, particularly the theoretical and empirical findings that characterize specific distributions. We introduce a novel and rigorous methodology, the Boosted Generalized Normal Distribution ($b$GND), to address these challenges. The Generalized Normal Distribution (GND) encompasses a wide range of parametric distributions commonly encountered in operations, and $b$GND leverages gradient boosting with tree learners to flexibly estimate the parameters of the GND as functions of covariates. We establish $b$GND's statistical consistency, thereby extending this key property to special cases studied in the ML literature that lacked such guarantees. Using data from a large academic emergency department in the United States, we show that the distributional forecasting of patient wait and service times can be meaningfully improved by leveraging findings from the healthcare operations literature. Specifically, $b$GND performs 6% and 9% better than the distribution-agnostic ML benchmark used to forecast wait and service times respectively. Further analysis suggests that these improvements translate into a 9% increase in patient satisfaction and a 4% reduction in mortality for myocardial infarction patients. Our work underscores the importance of integrating ML with operations knowledge to enhance distributional forecasts.