Bayesian Hierarchical Invariant Prediction

Abstract: We propose Bayesian Hierarchical Invariant Prediction (BHIP) reframing Invariant Causal Prediction (ICP) through the lens of Hierarchical Bayes. We leverage the hierarchical structure to explicitly test invariance of causal mechanisms under heterogeneous data, resulting in improved computational scalability for a larger number of predictors compared to ICP. Moreover, given its Bayesian nature BHIP enables the use of prior information. In this paper, we test two sparsity inducing priors: horseshoe and spike-and-slab, both of which allow us a more reliable identification of causal features. We test BHIP in synthetic and real-world data showing its potential as an alternative inference method to ICP.