# A concave pairwise fusion approach to subgroup analysis

arXiv: https://arxiv.org/abs/1508.07045 · HTML: https://mlsanity.com/paper/1508.07045/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2015.

## Built on by (most cited first, 16 of 16)

- [A Tree-based Model Averaging Approach for Personalized Treatment Effect Estimation from Heterogeneous Data Sources](https://mlsanity.com/paper/2103.06261/) (2021)
- [Reinforcement Learning with Heterogeneous Data: Estimation and Inference](https://mlsanity.com/paper/2202.00088/) (2022)
- [Clustered Federated Learning based on Nonconvex Pairwise Fusion](https://mlsanity.com/paper/2211.04218/) (2022)
- [Doubly Robust Fusion of Many Treatments for Policy Learning](https://mlsanity.com/paper/2505.08092/) (2025)
- [Multi-task Learning for Heterogeneous Multi-source Block-Wise Missing Data](https://mlsanity.com/paper/2505.24413/) (2025)
- [Simultaneous Heterogeneity and Reduced-rank Learning for Multivariate Response Regression](https://mlsanity.com/paper/2512.06514/) (2025)
- [Modelling Heterogeneity Using Bayesian Structured Sparsity](https://mlsanity.com/paper/2103.15919/) (2021)
- [Supervised Homogeneity Fusion: a Combinatorial Approach](https://mlsanity.com/paper/2201.01036/) (2022)
- [Coefficient Shape Alignment in Multiple Functional Linear Regression](https://mlsanity.com/paper/2312.01925/) (2023)
- [Coefficient Shape Transfer Learning for Functional Linear Regression](https://mlsanity.com/paper/2506.11367/) (2025)
- [Federated Online Learning for Heterogeneous Multisource Streaming Data](https://mlsanity.com/paper/2508.06652/) (2025)
- [Row-wise Fusion Regularization: An Interpretable Personalized Federated Learning Framework in Large-Scale Scenarios](https://mlsanity.com/paper/2510.14413/) (2025)
- [Robust Subgroup Analysis for Heterogeneous Censored Data](https://mlsanity.com/paper/2607.11389/) (2026)
- [Multitask Regression with Pairwise Fusion](https://mlsanity.com/paper/2609.27280/) (2026)
- [Co-Supervised Tree Synthesis for Interpretable Subgroup Identification and Honest Treatment Effect Inference in Randomized Trials](https://mlsanity.com/paper/2610.03927/) (2026)
- [Neural Supervised Clustering for Learning Individualized Treatment Rules with Many Treatments](https://mlsanity.com/paper/2610.19104/) (2026)

## Abstract (arXiv)

An important step in developing individualized treatment strategies is to correctly identify subgroups of a heterogeneous population, so that specific treatment can be given to each subgroup. In this paper, we consider the situation with samples drawn from a population consisting of subgroups with different means, along with certain covariates. We propose a penalized approach for subgroup analysis based on a regression model, in which heterogeneity is driven by unobserved latent factors and thus can be represented by using subject-specific intercepts. We apply concave penalty functions to pairwise differences of the intercepts. This procedure automatically divides the observations into subgroups. We develop an alternating direction method of multipliers algorithm with concave penalties to implement the proposed approach and demonstrate its convergence. We also establish the theoretical properties of our proposed estimator and determine the order requirement of the minimal difference of signals between groups in order to recover them. These results provide a sound basis for making statistical inference in subgroup analysis. Our proposed method is further illustrated by simulation studies and analysis of the Cleveland heart disease dataset.