# Bayesian Variable Selection for Multi-Outcome Models Through Shared Shrinkage

arXiv: https://arxiv.org/abs/1904.11594 · HTML: https://mlsanity.com/paper/1904.11594/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2019.

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

- [Infinite-dimensional optimization and Bayesian nonparametric learning of stochastic differential equations](https://mlsanity.com/paper/2205.15368/) (2022)
- [Deep Multitask Learning for Mixed-Type Outcomes with Shared Sparsity](https://mlsanity.com/paper/2607.00995/) (2026)

## Abstract (arXiv)

Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly sparse) vector with a few non-zero components, those covariates that are most important. This article extends the global-local shrinkage idea to a scenario where one wishes to model multiple response variables simultaneously. Here, we have developed a variable selection method for a K-outcome model (multivariate regression) that identifies the most important covariates across all outcomes. The prior for all regression coefficients is a mean zero normal with coefficient-specific variance term that consists of a predictor-specific factor (shared local shrinkage parameter) and a model-specific factor (global shrinkage term) that differs in each model. The performance of our modeling approach is evaluated through simulation studies and a data example.