# An ADMM approach for multi-response regression with overlapping groups and interaction effects

arXiv: https://arxiv.org/abs/2303.11155 · HTML: https://mlsanity.com/paper/2303.11155/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 27 references that are in the map.
- First posted on arXiv 20 Mar 2023.

## Builds on (most cited first, 5 of 5)

- [Convex Modeling of Interactions with Strong Heredity](https://mlsanity.com/paper/1410.3517/) (2014)
- [A Pliable Lasso](https://mlsanity.com/paper/1712.00484/) (2017)
- [Structured penalized regression for drug sensitivity prediction](https://mlsanity.com/paper/1902.04996/) (2019)
- [Parameter Estimation with the Ordered ℓ2 Regularization via an Alternating Direction Method of Multipliers](https://mlsanity.com/paper/1909.01519/) (2019)
- [Doubly structured sparsity for grouped multivariate responses with application to functional outcome score modeling](https://mlsanity.com/paper/2302.11098/) (2023)

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

- [PliableBVS: A flexible Bayesian variable selection method for modeling interactions with mandatory modifying variables](https://mlsanity.com/paper/2606.02017/) (2026)

## Abstract (arXiv)

In this paper, we consider the regularized multi-response regression problem where there exists some structural relation within the responses and also between the covariates and a set of modifying variables. To handle this problem, we propose MADMMplasso, a novel regularized regression method. This method is able to find covariates and their corresponding interactions, with some joint association with multiple related responses. We allow the interaction term between covariate and modifying variable to be included in a (weak) asymmetrical hierarchical manner by first considering whether the corresponding covariate main term is in the model. For parameter estimation, we develop an ADMM algorithm that allows us to implement the overlapping groups in a simple way. The results from the simulations and analysis of a pharmacogenomic screen data set show that the proposed method has an advantage in handling correlated responses and interaction effects, both with respect to prediction and variable selection performance.