BaGGLS: a Bayesian shrinkage framework for interpretable modeling of interactions in high-dimensional biological data

Motivation: Biological data is often high dimensional, noisy, and governed by complex interactions among sparse signals. This poses major challenges for interpretability and reliable feature selection. Tasks such as identifying motif interactions in genomics exemplify these difficulties, as only a small subset of biologically relevant features (e.g. motifs) are typically active, and their effects are often non-linear and context-dependent. While statistical approaches often result in more interpretable models, deep learning models have proven effective in modeling complex interactions and prediction accu-
racy, yet their black-box nature limits interpretability.

Results: We introduce BaGGLS, a flexible and interpretable probabilistic binary regression model designed for highdimensional biological inference involving feature interactions. BaGGLS incorporates a Bayesian group global-local shrinkage prior, aligned with the group structure introduced by interaction terms. This prior encourages sparsity while retaining interpretability, helping to isolate meaningful signals and suppress noise. To enable scalable inference, we employ a partially factorized variational approximation that captures posterior skewness and supports efficient learning even in large
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feature spaces. In extensive simulations, we compare BaGGLS to frequentist probit regressions (unconstrained and with L1-penalty) as well as a probit model with Markov Chain Monte Carlo (MCMC) sampling under a horseshoe prior. We can show that BaGGLS outperforms the other methods with regard to interaction detection and is many times faster than MCMC sampling under the horseshoe prior. We also demonstrate the usefulness of BaGGLS in the context of interaction discovery from motif scanner outputs (e.g. Find Individual Motif Occurrences (FIMO)) and noisy attribution scores from deep learning models. This shows that BaGGLS is a promising approach for uncovering biologically relevant interaction patterns, with potential applicability across a range of high-dimensional tasks in computational biology.