# PliableBVS: A flexible Bayesian variable selection method for modeling interactions with mandatory modifying variables

arXiv: https://arxiv.org/abs/2606.02017 · HTML: https://mlsanity.com/paper/2606.02017/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 60 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 6 of 6)

- [Cooperative learning for multiview analysis](https://mlsanity.com/paper/2112.12337/) (2021)
- [The Kernel Interaction Trick: Fast Bayesian Discovery of Pairwise Interactions in High Dimensions](https://mlsanity.com/paper/1905.06501/) (2019)
- [A Pliable Lasso](https://mlsanity.com/paper/1712.00484/) (2017)
- [Multivariate Bayesian structured variable selection for pharmacogenomic studies](https://mlsanity.com/paper/2101.05899/) (2021)
- [An ADMM approach for multi-response regression with overlapping groups and interaction effects](https://mlsanity.com/paper/2303.11155/) (2023)
- [Linked shrinkage to improve estimation of interaction effects in regression models](https://mlsanity.com/paper/2309.13998/) (2023)

## Abstract (arXiv)

High-dimensional interaction models are useful for studying, for example, how a large set of variables of interest, such as gene expression or other omics features, interact with a smaller set of modifying variables, such as clinical covariates. In this context, the pliable lasso has recently been proposed as an efficient method for screening large numbers of potential interaction terms under an asymmetric weak hierarchical constraint. In this work, we extend this framework by introducing PliableBVS, a Bayesian variable selection approach that preserves the hierarchical structure of the pliable lasso while inducing sparsity through spike-and-slab priors. The proposed model combines the continuous shrinkage effect of Bayesian lasso with a hierarchical spike-and-slab prior formulation that has two layers of decision variables: one governing the inclusion of main effects and another controlling the inclusion of interaction effects which is conditional on the inclusion of the corresponding main effects. This structure enables simultaneous selection of high-dimensional main and interaction effects within a coherent probabilistic framework. In simulation studies the proposed method outperforms the original pliable lasso in identifying active main and interaction effects, reducing false discoveries, and improving prediction accuracy in most scenarios. Applications with data from a labor onset study and a preeclampsia study demonstrate that PliableBVS selects biologically meaningful features and interactions.