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Bayesian Hierarchical Invariant Prediction

arXiv stat.ML / 4/7/2026

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Key Points

  • The paper introduces Bayesian Hierarchical Invariant Prediction (BHIP) as a Bayesian re-framing of Invariant Causal Prediction (ICP) using a hierarchical Bayes formulation.
  • BHIP tests whether causal mechanisms remain invariant across heterogeneous data while explicitly leveraging hierarchical structure to improve computational scalability with more predictors.
  • Because BHIP is Bayesian, it supports incorporating prior information, which ICP-style methods may not directly provide in the same way.
  • The authors evaluate BHIP on synthetic and real-world datasets and find evidence that it can serve as an alternative inference approach to ICP and related methods.
  • Overall, the work aims to make invariant causal inference more scalable and more flexible by combining invariance testing with Bayesian modeling.

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. We evaluate BHIP on both synthetic and real-world datasets, demonstrating its potential as an alternative inference method to ICP and related methods.

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