When Not to Correct: Evidence-Based Interaction Prediction for Combinatorial Perturbations

Predicting the transcriptomic effects of unseen combinatorial genetic perturbations from observed single-gene responses is a central challenge in functional genomics. A key difficulty is not whether genetic interactions exist, but whether interaction structure learned from observed pairs transfers reliably to new combinations. We introduce Hierarchical Null Regression (HNR), an evidence-based framework that adds interaction corrections only when supported by the training data. HNR separates residual interactions into a low-rank Core and full-rank Tail, with structure selected by permutation testing and predictions regularized through empirical Bayes estimation and uncertainty-aware shrinkage. When transferable structure is unsupported, HNR suppresses the interaction correction rather than forcing it. Across four Perturb-seq datasets, HNR consistently improves prediction of unseen combinations over strong linear, neural, graph-based, and pretrained baselines, while requiring no pretraining, external knowledge graph, validation-set hyperparameter tuning, or GPU computation. These results suggest that reliable combinatorial perturbation prediction depends not only on modeling interactions, but on determining when those interactions can be trusted. Code is provided as supplemental material for review and will be publicly released upon acceptance.