# Selective Inference for Group-Sparse Linear Models

arXiv: https://arxiv.org/abs/1607.08211 · HTML: https://mlsanity.com/paper/1607.08211/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2016.

## Built on by (most cited first, 21 of 21)

- [More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming](https://mlsanity.com/paper/2105.04920/) (2021)
- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [Valid P-Value for Deep Learning-Driven Salient Region](https://mlsanity.com/paper/2301.02437/) (2023)
- [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)
- [CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inference](https://mlsanity.com/paper/2310.14608/) (2023)
- [Exact Statistical Inference for the Wasserstein Distance by Selective Inference](https://mlsanity.com/paper/2109.14206/) (2021)
- [Exact Selective Inference with Randomization](https://mlsanity.com/paper/2212.12940/) (2022)
- [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)
- [Statistical Inference for Feature Selection after Optimal Transport-based Domain Adaptation](https://mlsanity.com/paper/2410.15022/) (2024)
- [Controllable RANSAC-based Anomaly Detection via Hypothesis Testing](https://mlsanity.com/paper/2410.15133/) (2024)
- [Statistical Inference for Autoencoder-based Anomaly Detection after Representation Learning-based Domain Adaptation](https://mlsanity.com/paper/2508.07049/) (2025)
- [Bounded P-values in Parametric Programming-based Selective Inference](https://mlsanity.com/paper/2307.11351/) (2023)
- [Statistical Test for Diffusion-Based Anomaly Localization via Selective Inference](https://mlsanity.com/paper/2402.11789/) (2024)
- [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)
- [Post-Transfer Learning Statistical Inference in High-Dimensional Regression](https://mlsanity.com/paper/2504.18212/) (2025)
- [φ-Table: A Statistical Explanation for Global SHAP](https://mlsanity.com/paper/2512.07578/) (2025)
- [Post-Anomaly Detection Inference for Deep SVDD](https://mlsanity.com/paper/2609.37935/) (2026)

## Abstract (arXiv)

We develop tools for selective inference in the setting of group sparsity, including the construction of confidence intervals and p-values for testing selected groups of variables. Our main technical result gives the precise distribution of the magnitude of the projection of the data onto a given subspace, and enables us to develop inference procedures for a broad class of group-sparse selection methods, including the group lasso, iterative hard thresholding, and forward stepwise regression. We give numerical results to illustrate these tools on simulated data and on health record data.