# Splitting strategies for post-selection inference

arXiv: https://arxiv.org/abs/2102.02159 · HTML: https://mlsanity.com/paper/2102.02159/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2021.

## Built on by (most cited first, 16 of 16)

- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [Data fission: splitting a single data point](https://mlsanity.com/paper/2112.11079/) (2021)
- [Data thinning for convolution-closed distributions](https://mlsanity.com/paper/2301.07276/) (2023)
- [Valid Inference After Causal Discovery](https://mlsanity.com/paper/2208.05949/) (2022)
- [Generalized Data Thinning Using Sufficient Statistics](https://mlsanity.com/paper/2303.12931/) (2023)
- [A Flexible Defense Against the Winner's Curse](https://mlsanity.com/paper/2411.18569/) (2024)
- [Exact Selective Inference with Randomization](https://mlsanity.com/paper/2212.12940/) (2022)
- [Calibrating Decision Robustness via Inverse Conformal Risk Control](https://mlsanity.com/paper/2510.07750/) (2025)
- [Selective inference using randomized group lasso estimators for general models](https://mlsanity.com/paper/2306.13829/) (2023)
- [Decomposing Gaussians with Unknown Covariance](https://mlsanity.com/paper/2409.11497/) (2024)
- [Thinning a Wishart Random Matrix](https://mlsanity.com/paper/2502.09957/) (2025)
- [Flexible Selective Inference with Flow-based Transport Maps](https://mlsanity.com/paper/2506.01150/) (2025)
- [Hierarchical Clustering With Confidence](https://mlsanity.com/paper/2512.06522/) (2025)
- [Testing hypotheses via orthogonalization](https://mlsanity.com/paper/2606.29732/) (2026)
- [Screening Collapse under Recursive Synthetic Data](https://mlsanity.com/paper/2610.15617/) (2026)
- [Selective Inference for Clustering Under Unknown Covariance](https://mlsanity.com/paper/2610.17458/) (2026)

## Abstract (arXiv)

We consider the problem of providing valid inference for a selected parameter in a sparse regression setting. It is well known that classical regression tools can be unreliable in this context due to the bias generated in the selection step. Many approaches have been proposed in recent years to ensure inferential validity. Here, we consider a simple alternative to data splitting based on randomising the response vector, which allows for higher selection and inferential power than the former and is applicable with an arbitrary selection rule. We provide a theoretical and empirical comparison of both methods and derive a Central Limit Theorem for the randomisation approach. Our investigations show that the gain in power can be substantial.