# Soft Maximin Estimation for Heterogeneous Data

arXiv: https://arxiv.org/abs/1805.02407 · HTML: https://mlsanity.com/paper/1805.02407/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2018.

## Built on by (most cited first, 1 of 1)

- [Maximum Risk Minimization with Random Forests](https://mlsanity.com/paper/2512.10445/) (2025)

## Abstract (arXiv)

Extracting a common robust signal from data divided into heterogeneous groups can be difficult when each group -- in addition to the signal -- can contain large, unique variation components. Previously, maximin estimation has been proposed as a robust estimation method in the presence of heterogeneous noise. We propose soft maximin estimation as a computationally attractive alternative aimed at striking a balance between pooled estimation and (hard) maximin estimation. The soft maximin method provides a range of estimators, controlled by a parameter zeta>0, that interpolates pooled least squares estimation and maximin estimation. By establishing relevant theoretical properties we argue that the soft maximin method is both statistically sensibel and computationally attractive. We also demonstrate, on real and simulated data, that the soft maximin estimator can offer improvements over both pooled OLS and hard maximin in terms of predictive performance and computational complexity. A time and memory efficient implementation is provided in the R package verb+SMME+ available on CRAN.