An introduction to (isotonic) subgroup selection 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, I’ll introduce 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 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 we select to be as large as possible. In this talk, I will give a general overview of the topic, and then introduce our algorithm for isotonic subgroup selection for settings in which the regression function is coordinate-wise increasing in the individual covariates. Some of the talk will focus on material in our paper “Isotonic Subgroup Selection” see: https://arxiv.org/abs/2305.04852 This article was published on 2025-10-29
