Invariance-based inference (or invariant inference) is a method for testing and inference based solely on data invariance assumptions; e.g., inference assuming only exchangeability of regression errors, or sign symmetry, or both. Compared to the classical “i.i.d. data framework”, invariance-based inference is simpler and provides a seamless connection between experimental and observational studies.

Papers

• Invariance-based inference in high-dimensional regression with finite-sample guarantees
  with Guo, W. (2025+). R&R.

• Asymptotic validity and finite-sample properties of approximate randomization tests — R package code slides
  Biometrika, 2025, asaf085. Prior but longer versions previously arxived as:

  • “Life After Bootstrap: Residual Randomization Inference in Regression Models” in 2019. slides

  • “Invariant Inference via Residual Randomization” in 2022.

• Robust inference for high-dimensional linear models via residual randomization
  with Wang, S., Lee S.K., Kolar, M. (2021). International Conference on Machine Learning (ICML), oral.

Toulis, P. (2019). Randomization Inference in Regression Models — R Package RRI. (Technical report) pdf

Code

RRI R package:

—on CRAN: https://cran.r-project.org/package=RRI

—on GitHub: https://github.com/ptoulis/residual-randomization