# Exact Selective Inference with Randomization

arXiv: https://arxiv.org/abs/2212.12940 · HTML: https://mlsanity.com/paper/2212.12940/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 25 Dec 2022.

## Builds on (most cited first, 21 of 21)

- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [Selective Inference for Hierarchical Clustering](https://mlsanity.com/paper/2012.02936/) (2020)
- [SLOPE - Adaptive variable selection via convex optimization](https://mlsanity.com/paper/1407.3824/) (2014)
- [Valid Inference Corrected for Outlier Removal](https://mlsanity.com/paper/1711.10635/) (2017)
- [Computing Valid p-value for Optimal Changepoint by Selective Inference using Dynamic Programming](https://mlsanity.com/paper/2002.09132/) (2020)
- [More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming](https://mlsanity.com/paper/2105.04920/) (2021)
- [Computing Valid p-values for Image Segmentation by Selective Inference](https://mlsanity.com/paper/1906.00629/) (2019)
- [More powerful post-selection inference, with application to the Lasso](https://mlsanity.com/paper/1801.09037/) (2018)
- [Selective Inference for Group-Sparse Linear Models](https://mlsanity.com/paper/1607.08211/) (2016)
- [Splitting strategies for post-selection inference](https://mlsanity.com/paper/2102.02159/) (2021)
- [Exact Post Model Selection Inference for Marginal Screening](https://mlsanity.com/paper/1402.5596/) (2014)
- [Approximate selective inference via maximum likelihood](https://mlsanity.com/paper/1902.07884/) (2019)
- [Post-Selection Inference via Algorithmic Stability](https://mlsanity.com/paper/2011.09462/) (2020)
- [More powerful selective inference for the graph fused lasso](https://mlsanity.com/paper/2109.10451/) (2021)
- [Multicarving for high-dimensional post-selection inference](https://mlsanity.com/paper/2006.04613/) (2020)
- [A (tight) upper bound for the length of confidence intervals with conditional coverage](https://mlsanity.com/paper/2007.12448/) (2020)
- [Approximate Post-Selective Inference for Regression with the Group LASSO](https://mlsanity.com/paper/2012.15664/) (2020)
- [Inference after latent variable estimation for single-cell RNA sequencing data](https://mlsanity.com/paper/2207.00554/) (2022)
- [Integrative Bayesian models using Post-selective Inference: a case study in Radiogenomics](https://mlsanity.com/paper/2004.12012/) (2020)
- [Valid Post-selection Inference in Assumption-lean Linear Regression](https://mlsanity.com/paper/1806.04119/) (2018)
- [An MCMC-free approach to post-selective inference](https://mlsanity.com/paper/1703.06154/) (2017)

## Built on by (most cited first, 6 of 6)

- [Selective Inference for Changepoint detection by Recurrent Neural Network](https://mlsanity.com/paper/2311.14964/) (2023)
- [Selective inference using randomized group lasso estimators for general models](https://mlsanity.com/paper/2306.13829/) (2023)
- [Bounded P-values in Parametric Programming-based Selective Inference](https://mlsanity.com/paper/2307.11351/) (2023)
- [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)

## Abstract (arXiv)

We introduce a pivot for exact selective inference with randomization. Not only does our pivot lead to exact inference in Gaussian regression models, but it is also available in closed form. We reduce the problem of exact selective inference to a bivariate truncated Gaussian distribution. By doing so, we give up some power that is achieved with approximate maximum likelihood estimation in Panigrahi and Taylor (2022). Yet our pivot always produces narrower confidence intervals than a closely related data splitting procedure. We investigate the trade-off between power and exact selective inference on simulated datasets and an HIV drug resistance dataset.