# More powerful post-selection inference, with application to the Lasso

arXiv: https://arxiv.org/abs/1801.09037 · HTML: https://mlsanity.com/paper/1801.09037/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2018.

## Built on by (most cited first, 23 of 23)

- [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)
- [Fast and More Powerful Selective Inference for Sparse High-order Interaction Model](https://mlsanity.com/paper/2106.04929/) (2021)
- [Tree-Values: selective inference for regression trees](https://mlsanity.com/paper/2106.07816/) (2021)
- [Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inference](https://mlsanity.com/paper/2110.08989/) (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 Attention Map in Vision Transformer](https://mlsanity.com/paper/2401.08169/) (2024)
- [Selective Inference for Changepoint detection by Recurrent Neural Network](https://mlsanity.com/paper/2311.14964/) (2023)
- [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)
- [Change Point Detection in the Frequency Domain with Statistical Reliability](https://mlsanity.com/paper/2502.03062/) (2025)
- [Statistical Inference for Autoencoder-based Anomaly Detection after Representation Learning-based Domain Adaptation](https://mlsanity.com/paper/2508.07049/) (2025)
- [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)
- [Post-Transfer Learning Statistical Inference in High-Dimensional Regression](https://mlsanity.com/paper/2504.18212/) (2025)
- [Statistical Inference for Clustering-based Anomaly Detection](https://mlsanity.com/paper/2504.18633/) (2025)
- [Finite-Sample Inference for Sparsely Permuted Linear Regression](https://mlsanity.com/paper/2601.14872/) (2026)
- [Post-ADC Inference: Valid Inference After Active Data Collection](https://mlsanity.com/paper/2605.11511/) (2026)

## Abstract (arXiv)

Investigators often use the data to generate interesting hypotheses and then perform inference for the generated hypotheses. P-values and confidence intervals must account for this explorative data analysis. A fruitful method for doing so is to condition any inferences on the components of the data used to generate the hypotheses, thus preventing information in those components from being used again. Some currently popular methods "over-condition", leading to wide intervals. We show how to perform the minimal conditioning in a computationally tractable way. In high dimensions, even this minimal conditioning can lead to intervals that are too wide to be useful, suggesting that up to now the cost of hypothesis generation has been underestimated. We show how to generate hypotheses in a strategic manner that sharply reduces the cost of data exploration and results in useful confidence intervals. Our discussion focuses on the problem of post-selection inference after fitting a lasso regression model, but we also outline its extension to a much more general setting.