A Cluster Elastic Net for Multivariate Regression
This work addresses the need for efficient multivariate regression methods in fields like genomics and business operations, though it appears incremental as it builds on existing penalized regression techniques.
The authors tackled the problem of estimating coefficients in multivariate regression with clustered response variables by proposing a method that incorporates a fusion penalty for within-cluster shrinkage and an L1 penalty for variable selection, applicable to both known and unknown clustering structures, and demonstrated its effectiveness through simulations and data examples in business operations and genomics.
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.