# Approximate selective inference via maximum likelihood

arXiv: https://arxiv.org/abs/1902.07884 · HTML: https://mlsanity.com/paper/1902.07884/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2019.

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

- [Exact Selective Inference with Randomization](https://mlsanity.com/paper/2212.12940/) (2022)
- [Selective inference using randomized group lasso estimators for general models](https://mlsanity.com/paper/2306.13829/) (2023)
- [Black-box Selective Inference via Bootstrapping](https://mlsanity.com/paper/2203.14504/) (2022)
- [Selective Inference for Sparse Multitask Regression with Applications in Neuroimaging](https://mlsanity.com/paper/2205.14220/) (2022)
- [Bounded P-values in Parametric Programming-based Selective Inference](https://mlsanity.com/paper/2307.11351/) (2023)
- [Statistical Inference for the Dynamic Time Warping Distance, with Application to Abnormal Time-Series Detection](https://mlsanity.com/paper/2202.06593/) (2022)
- [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)

## Abstract (arXiv)

Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference framework for Gaussian data. We propose a new method for inference through approximate maximum likelihood estimation. Our goal is to: (i) achieve better inferential power with the aid of randomization, (ii) bypass expensive MCMC sampling from exact conditional distributions that are hard to evaluate in closed forms. We construct approximate inference, e.g., p-values, confidence intervals etc., by solving a fairly simple, convex optimization problem. We illustrate the potential of our method across wide-ranging values of signal-to-noise ratio in simulations. On a cancer gene expression data set we find that our method improves upon the inferential power of some commonly used strategies for selective inference.