# A Scale-free Approach for False Discovery Rate Control in Generalized Linear Models

arXiv: https://arxiv.org/abs/2007.01237 · HTML: https://mlsanity.com/paper/2007.01237/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2020.

## Built on by (most cited first, 8 of 8)

- [Near-optimal multiple testing in Bayesian linear models with finite-sample FDR control](https://mlsanity.com/paper/2211.02778/) (2022)
- [Selective inference using randomized group lasso estimators for general models](https://mlsanity.com/paper/2306.13829/) (2023)
- [Provable FDR Control for Deep Feature Selection: Deep MLPs and Beyond](https://mlsanity.com/paper/2512.04696/) (2025)
- [High-dimensional Inference and FDR Control for Simulated Markov Random Fields](https://mlsanity.com/paper/2202.05612/) (2022)
- [CatNet: Controlling the False Discovery Rate in LSTM with SHAP Feature Importance and Gaussian Mirrors](https://mlsanity.com/paper/2411.16666/) (2024)
- [False Discovery Rate Control via Bayesian Mirror Statistic](https://mlsanity.com/paper/2510.00875/) (2025)
- [Model-Agnostic FDR Control via Group Gaussian Mirror and Permutation SHAP](https://mlsanity.com/paper/2608.00989/) (2026)
- [Mitigating Object Hallucination in Large Vision-Language Models via False Discovery Controlled Visual Data Splitting](https://mlsanity.com/paper/2609.38979/) (2026)

## Abstract (arXiv)

The generalized linear models (GLM) have been widely used in practice to model non-Gaussian response variables. When the number of explanatory features is relatively large, scientific researchers are of interest to perform controlled feature selection in order to simplify the downstream analysis. This paper introduces a new framework for feature selection in GLMs that can achieve false discovery rate (FDR) control in two asymptotic regimes. The key step is to construct a mirror statistic to measure the importance of each feature, which is based upon two (asymptotically) independent estimates of the corresponding true coefficient obtained via either the data-splitting method or the Gaussian mirror method. The FDR control is achieved by taking advantage of the mirror statistic's property that, for any null feature, its sampling distribution is (asymptotically) symmetric about 0. In the moderate-dimensional setting in which the ratio between the dimension (number of features) p and the sample size n converges to a fixed value, we construct the mirror statistic based on the maximum likelihood estimation. In the high-dimensional setting where p is much larger than n, we use the debiased Lasso to build the mirror statistic. Compared to the Benjamini-Hochberg procedure, which crucially relies on the asymptotic normality of the Z statistic, the proposed methodology is scale free as it only hinges on the symmetric property, thus is expected to be more robust in finite-sample cases. Both simulation results and a real data application show that the proposed methods are capable of controlling the FDR, and are often more powerful than existing methods including the Benjamini-Hochberg procedure and the knockoff filter.