# A Huber loss-based super learner with applications to healthcare expenditures

arXiv: https://arxiv.org/abs/2205.06870 · HTML: https://mlsanity.com/paper/2205.06870/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 39 references that are in the map.
- First posted on arXiv 13 May 2022.

## Builds on (most cited first, 2 of 2)

- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [Fair Regression for Health Care Spending](https://mlsanity.com/paper/1901.10566/) (2019)

## Abstract (arXiv)

Complex distributions of the healthcare expenditure pose challenges to statistical modeling via a single model. Super learning, an ensemble method that combines a range of candidate models, is a promising alternative for cost estimation and has shown benefits over a single model. However, standard approaches to super learning may have poor performance in settings where extreme values are present, such as healthcare expenditure data. We propose a super learner based on the Huber loss, a "robust" loss function that combines squared error loss with absolute loss to down-weight the influence of outliers. We derive oracle inequalities that establish bounds on the finite-sample and asymptotic performance of the method. We show that the proposed method can be used both directly to optimize Huber risk, as well as in finite-sample settings where optimizing mean squared error is the ultimate goal. For this latter scenario, we provide two methods for performing a grid search for values of the robustification parameter indexing the Huber loss. Simulations and real data analysis demonstrate appreciable finite-sample gains in cost prediction and causal effect estimation using our proposed method.