# Selective inference in regression models with groups of variables

arXiv: https://arxiv.org/abs/1511.01478 · HTML: https://mlsanity.com/paper/1511.01478/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2015.

## Built on by (most cited first, 9 of 9)

- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuation](https://mlsanity.com/paper/2104.10840/) (2021)
- [Fast and More Powerful Selective Inference for Sparse High-order Interaction Model](https://mlsanity.com/paper/2106.04929/) (2021)
- [Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inference](https://mlsanity.com/paper/2110.08989/) (2021)
- [Exact Statistical Inference for the Wasserstein Distance by Selective Inference](https://mlsanity.com/paper/2109.14206/) (2021)
- [Change Point Detection in the Frequency Domain with Statistical Reliability](https://mlsanity.com/paper/2502.03062/) (2025)
- [Statistical Inference for the Dynamic Time Warping Distance, with Application to Abnormal Time-Series Detection](https://mlsanity.com/paper/2202.06593/) (2022)
- [Inferring independent sets of Gaussian variables after thresholding correlations](https://mlsanity.com/paper/2211.01521/) (2022)
- [Neural Networks beyond explainability: Selective inference for sequence motifs](https://mlsanity.com/paper/2212.12542/) (2022)

## Abstract (arXiv)

We provide a general mathematical framework for selective inference with supervised model selection procedures characterized by quadratic forms in the outcome variable. Forward stepwise with groups of variables is an important special case as it allows models with categorical variables or factors. Models can be chosen by AIC, BIC, or a fixed number of steps. We provide an exact significance test for each group of variables in the selected model based on an appropriately truncated chi or F distribution for the cases of known and unknown σ2 respectively. An efficient software implementation is available as a package in the R statistical programming language.