# Selective inference using randomized group lasso estimators for general models

arXiv: https://arxiv.org/abs/2306.13829 · HTML: https://mlsanity.com/paper/2306.13829/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 49 references that are in the map.
- First posted on arXiv 24 Jun 2023.

## Builds on (most cited first, 17 of 17)

- [A modern maximum-likelihood theory for high-dimensional logistic regression](https://mlsanity.com/paper/1803.06964/) (2018)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming](https://mlsanity.com/paper/2105.04920/) (2021)
- [Smoothed Quantile Regression with Large-Scale Inference](https://mlsanity.com/paper/2012.05187/) (2020)
- [Splitting strategies for post-selection inference](https://mlsanity.com/paper/2102.02159/) (2021)
- [The Likelihood Ratio Test in High-Dimensional Logistic Regression Is Asymptotically a Rescaled Chi-Square](https://mlsanity.com/paper/1706.01191/) (2017)
- [Data fission: splitting a single data point](https://mlsanity.com/paper/2112.11079/) (2021)
- [Approximate selective inference via maximum likelihood](https://mlsanity.com/paper/1902.07884/) (2019)
- [A Scale-free Approach for False Discovery Rate Control in Generalized Linear Models](https://mlsanity.com/paper/2007.01237/) (2020)
- [Generalized Data Thinning Using Sufficient Statistics](https://mlsanity.com/paper/2303.12931/) (2023)
- [Exact Selective Inference with Randomization](https://mlsanity.com/paper/2212.12940/) (2022)
- [Post-selection inference for L1-penalized likelihood models](https://mlsanity.com/paper/1602.07358/) (2016)
- [Multicarving for high-dimensional post-selection inference](https://mlsanity.com/paper/2006.04613/) (2020)
- [Approximate Post-Selective Inference for Regression with the Group LASSO](https://mlsanity.com/paper/2012.15664/) (2020)
- [Integrative Bayesian models using Post-selective Inference: a case study in Radiogenomics](https://mlsanity.com/paper/2004.12012/) (2020)
- [Constructing confidence sets after lasso selection by randomized estimator augmentation](https://mlsanity.com/paper/1904.08018/) (2019)
- [Selective Inference with Distributed Data](https://mlsanity.com/paper/2301.06162/) (2023)

## Built on by (most cited first, 3 of 3)

- [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)
- [Interpretable AI with Local Distillation](https://mlsanity.com/paper/2608.23538/) (2026)

## Abstract (arXiv)

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for overdispersed count data, for example, and allows for categorical or grouped covariates as well as continuous covariates. A randomized group-regularized optimization problem is studied. The added randomization allows us to construct a post-selection likelihood which we show to be adequate for selective inference when conditioning on the event of the selection of the grouped covariates. This likelihood also provides a selective point estimator, accounting for the selection by the group lasso. Confidence regions for the regression parameters in the selected model take the form of Wald-type regions and are shown to have bounded volume. The selective inference method for grouped lasso is illustrated on data from the national health and nutrition examination survey while simulations showcase its behaviour and favorable comparison with other methods.