# A Cluster Elastic Net for Multivariate Regression

arXiv: https://arxiv.org/abs/1707.03530 · HTML: https://mlsanity.com/paper/1707.03530/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2017.

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

- [Sparse outlier-robust PCA for multi-source data](https://mlsanity.com/paper/2407.16299/) (2024)
- [On the Use of Minimum Penalties in Statistical Learning](https://mlsanity.com/paper/2106.05172/) (2021)

## Abstract (arXiv)

We propose a method for estimating coefficients in multivariate regression when there is a clustering structure to the response variables. The proposed method includes a fusion penalty, to shrink the difference in fitted values from responses in the same cluster, and an L1 penalty for simultaneous variable selection and estimation. The method can be used when the grouping structure of the response variables is known or unknown. When the clustering structure is unknown the method will simultaneously estimate the clusters of the response and the regression coefficients. Theoretical results are presented for the penalized least squares case, including asymptotic results allowing for p >> n. We extend our method to the setting where the responses are binomial variables. We propose a coordinate descent algorithm for both the normal and binomial likelihood, which can easily be extended to other generalized linear model (GLM) settings. Simulations and data examples from business operations and genomics are presented to show the merits of both the least squares and binomial methods.