Selecting interaction effects in additive models using I-priors

Abstract

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.

Haziq Jamil

Assistant Professor in Statistics

My research interests include statistical theory, methods and computation, with applications towards the social sciences.