# Optimal subgroup selection

arXiv: https://arxiv.org/abs/2109.01077 · HTML: https://mlsanity.com/paper/2109.01077/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 62 references that are in the map.
- First posted on arXiv 2 Sep 2021.

## Builds on (most cited first, 7 of 7)

- [Model-based Recursive Partitioning for Subgroup Analyses](https://mlsanity.com/paper/1605.04078/) (2016)
- [Robust Super-Level Set Estimation using Gaussian Processes](https://mlsanity.com/paper/1811.09977/) (2018)
- [Smoothness-Adaptive Contextual Bandits](https://mlsanity.com/paper/1910.09714/) (2019)
- [Density Level Sets: Asymptotics, Inference, and Visualization](https://mlsanity.com/paper/1504.05438/) (2015)
- [Intentional Control of Type I Error over Unconscious Data Distortion: a Neyman-Pearson Approach to Text Classification](https://mlsanity.com/paper/1802.02558/) (2018)
- [Bandwidth selection for kernel density estimators of multivariate level sets and highest density regions](https://mlsanity.com/paper/1806.00731/) (2018)
- [Minimax Hausdorff estimation of density level sets](https://mlsanity.com/paper/1905.02897/) (2019)

## Built on by (most cited first, 2 of 2)

- [Nonparametric inference under shape constraints: past, present and future](https://mlsanity.com/paper/2509.26040/) (2025)
- [High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods](https://mlsanity.com/paper/2308.16192/) (2023)

## Abstract (arXiv)

In clinical trials and other applications, we often see regions of the feature space that appear to exhibit interesting behaviour, but it is unclear whether these observed phenomena are reflected at the population level. Focusing on a regression setting, we consider the subgroup selection challenge of identifying a region of the feature space on which the regression function exceeds a pre-determined threshold. We formulate the problem as one of constrained optimisation, where we seek a low-complexity, data-dependent selection set on which, with a guaranteed probability, the regression function is uniformly at least as large as the threshold; subject to this constraint, we would like the region to contain as much mass under the marginal feature distribution as possible. This leads to a natural notion of regret, and our main contribution is to determine the minimax optimal rate for this regret in both the sample size and the Type I error probability. The rate involves a delicate interplay between parameters that control the smoothness of the regression function, as well as exponents that quantify the extent to which the optimal selection set at the population level can be approximated by families of well-behaved subsets. Finally, we expand the scope of our previous results by illustrating how they may be generalised to a treatment and control setting, where interest lies in the heterogeneous treatment effect.