Additive models with interactions have been considered extensively in the literature, using estimation methods such as splines or Gaussian process regression. We present an alternative empirical-Bayes approach to selecting interaction effects using the I-prior approach introduced by Bergsma (2020). Using a parsimonious formulation of hierarchical interaction spaces, model selection is simplified. Furthermore, we present an efficient EM algo- rithm for estimating key hyperparameters. Simulations for linear regressions indicate competitive performance with methods such as the lasso and Bayesian variable selection using spike and slab priors or g-priors. However, our methodology is more gen- eral and can also be used with interacting nonlinear regression functions.