Boosted generalized normal distributions: Integrating machine learning with operations knowledge

TL;DR

This paper introduces the Boosted Generalized Normal Distribution ($b$GND), a novel method combining machine learning and operations knowledge to improve distributional forecasts in operational settings, demonstrated with healthcare data.

Contribution

The paper develops $b$GND, a new methodology that integrates ML with operations literature, providing statistical consistency and improved distributional predictions.

Findings

$b$GND outperforms benchmarks by 6-9% in forecasting accuracy.

Improved forecasts lead to 9% higher patient satisfaction.

Enhanced predictions contribute to 4% lower mortality rates.

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.