# Simultaneous Heterogeneity and Reduced-rank Learning for Multivariate Response Regression

arXiv: https://arxiv.org/abs/2512.06514 · HTML: https://mlsanity.com/paper/2512.06514/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 47 references that are in the map.
- First posted on arXiv 6 Dec 2025.

## Builds on (most cited first, 8 of 8)

- [A concave pairwise fusion approach to subgroup analysis](https://mlsanity.com/paper/1508.07045/) (2015)
- [Robust Reduced Rank Regression](https://mlsanity.com/paper/1509.03938/) (2015)
- [Nonparametric Tests for Treatment Effect Heterogeneity with Duration Outcomes](https://mlsanity.com/paper/1612.02090/) (2016)
- [SOFAR: large-scale association network learning](https://mlsanity.com/paper/1704.08349/) (2017)
- [Multivariate Functional Regression via Nested Reduced-Rank Regularization](https://mlsanity.com/paper/2003.04786/) (2020)
- [A fusion learning method to subgroup analysis of Alzheimer's disease](https://mlsanity.com/paper/2103.06363/) (2021)
- [Simultaneous Estimation and Group Identification for Network Vector Autoregressive Model with Heterogeneous Nodes](https://mlsanity.com/paper/2209.12229/) (2022)
- [Parallel integrative learning for large-scale multi-response regression with incomplete outcomes](https://mlsanity.com/paper/2104.05076/) (2021)

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

- [Robust Subgroup Analysis for Heterogeneous Censored Data](https://mlsanity.com/paper/2607.11389/) (2026)

## Abstract (arXiv)

Heterogeneous data are now ubiquitous in many applications in which correctly identifying the subgroups from a heterogeneous population is critical. Although there is an increasing body of literature on subgroup detection, existing methods mainly focus on the univariate response setting. In this paper, we propose a joint heterogeneity and reduced-rank learning framework to simultaneously identify the subgroup structure and estimate the covariate effects for heterogeneous multivariate response regression. In particular, our approach uses rank-constrained pairwise fusion penalization and conducts the subgroup analysis without requiring prior knowledge regarding the individual subgroup memberships. We implement the proposed approach by an alternating direction method of multipliers (ADMM) algorithm and show its convergence. We also establish the asymptotic properties for the resulting estimators under mild and interpretable conditions. A predictive information criterion is proposed to select the rank of the coefficient matrix with theoretical support. The effectiveness of the proposed approach is demonstrated through simulation studies and a real data application.