# Exact Post Model Selection Inference for Marginal Screening

arXiv: https://arxiv.org/abs/1402.5596 · HTML: https://mlsanity.com/paper/1402.5596/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2014.

## Built on by (most cited first, 12 of 12)

- [Valid Inference After Causal Discovery](https://mlsanity.com/paper/2208.05949/) (2022)
- [Exact Selective Inference with Randomization](https://mlsanity.com/paper/2212.12940/) (2022)
- [Pessimistic Model Selection for Offline Deep Reinforcement Learning](https://mlsanity.com/paper/2111.14346/) (2021)
- [Statistical Test for Feature Selection Pipelines by Selective Inference](https://mlsanity.com/paper/2406.18902/) (2024)
- [Statistical Test for Auto Feature Engineering by Selective Inference](https://mlsanity.com/paper/2410.19768/) (2024)
- [Quantifying Statistical Significance of Deep Nearest Neighbor Anomaly Detection via Selective Inference](https://mlsanity.com/paper/2502.12978/) (2025)
- [Change Point Detection in the Frequency Domain with Statistical Reliability](https://mlsanity.com/paper/2502.03062/) (2025)
- [Statistical Test for Diffusion-Based Anomaly Localization via Selective Inference](https://mlsanity.com/paper/2402.11789/) (2024)
- [An Analysis of Selection Bias Issue for Online Advertising](https://mlsanity.com/paper/2206.03853/) (2022)
- [Inferring independent sets of Gaussian variables after thresholding correlations](https://mlsanity.com/paper/2211.01521/) (2022)
- [A parametric distribution for exact post-selection inference with data carving](https://mlsanity.com/paper/2305.12581/) (2023)
- [Automatic Statistical Test for Rationally Expressible Algorithms by Selective Inference, with Applications to Feature Selection](https://mlsanity.com/paper/2608.04667/) (2026)

## Abstract (arXiv)

We develop a framework for post model selection inference, via marginal screening, in linear regression. At the core of this framework is a result that characterizes the exact distribution of linear functions of the response y, conditional on the model being selected (``condition on selection" framework). This allows us to construct valid confidence intervals and hypothesis tests for regression coefficients that account for the selection procedure. In contrast to recent work in high-dimensional statistics, our results are exact (non-asymptotic) and require no eigenvalue-like assumptions on the design matrix X. Furthermore, the computational cost of marginal regression, constructing confidence intervals and hypothesis testing is negligible compared to the cost of linear regression, thus making our methods particularly suitable for extremely large datasets. Although we focus on marginal screening to illustrate the applicability of the condition on selection framework, this framework is much more broadly applicable. We show how to apply the proposed framework to several other selection procedures including orthogonal matching pursuit, non-negative least squares, and marginal screening+Lasso.