Invariance-based inference — or invariant inference, for short —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

Guo, W. and Toulis, P. (2024+). Invariance-based inference in high-dimensional regression with finite-sample guarantees. Submitted.

Toulis, P. (2024+). Asymptotic validity and finite-sample properties of approximate randomization tests. Revise and Resubmit.

Wang, S., Lee S.K., Kolar, M., Toulis, P. (2021). Robust inference for high-dimensional linear models via residual randomization. International Conference on Machine Learning (ICML’21), oral.

Toulis, P. (2019). Life after bootstrap: Residual randomization inference in regression models with complex error structure. (early draft) arxiv code slides

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