# Post-selection inference for L1-penalized likelihood models

arXiv: https://arxiv.org/abs/1602.07358 · HTML: https://mlsanity.com/paper/1602.07358/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2016.

## Built on by (most cited first, 5 of 5)

- [Selective inference using randomized group lasso estimators for general models](https://mlsanity.com/paper/2306.13829/) (2023)
- [Discovering Significant Topics from Legal Decisions with Selective Inference](https://mlsanity.com/paper/2401.01068/) (2024)
- [Adaptive Noisy Data Augmentation for Regularized Estimation and Inference in Generalized Linear Models](https://mlsanity.com/paper/2204.08574/) (2022)
- [Explainable Boosting Machines with Sparsity -- Maintaining Explainability in High-Dimensional Settings](https://mlsanity.com/paper/2311.07452/) (2023)
- [Online Selective Conformal Prediction with Asymmetric Rules: A Permutation Test Approach](https://mlsanity.com/paper/2602.10018/) (2026)

## Abstract (arXiv)

We present a new method for post-selection inference for L1 (lasso)-penalized likelihood models, including generalized regression models. Our approach generalizes the post-selection framework presented in Lee et al (2014). The method provides p-values and confidence intervals that are asymptotically valid, conditional on the inherent selection done by the lasso. We present applications of this work to (regularized) logistic regression, Cox's proportional hazards model and the graphical lasso.