# Black-box Selective Inference via Bootstrapping

arXiv: https://arxiv.org/abs/2203.14504 · HTML: https://mlsanity.com/paper/2203.14504/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 46 references that are in the map.
- First posted on arXiv 28 Mar 2022.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [A knockoff filter for high-dimensional selective inference](https://mlsanity.com/paper/1602.03574/) (2016)
- [More powerful post-selection inference, with application to the Lasso](https://mlsanity.com/paper/1801.09037/) (2018)
- [Approximate selective inference via maximum likelihood](https://mlsanity.com/paper/1902.07884/) (2019)
- [Selective inference for the problem of regions via multiscale bootstrap](https://mlsanity.com/paper/1711.00949/) (2017)
- [Multicarving for high-dimensional post-selection inference](https://mlsanity.com/paper/2006.04613/) (2020)
- [A (tight) upper bound for the length of confidence intervals with conditional coverage](https://mlsanity.com/paper/2007.12448/) (2020)
- [Selective inference with unknown variance via the square-root LASSO](https://mlsanity.com/paper/1504.08031/) (2015)
- [Bootstrap inference after using multiple queries for model selection](https://mlsanity.com/paper/1612.07811/) (2016)
- [Selective inference after feature selection via multiscale bootstrap](https://mlsanity.com/paper/1905.10573/) (2019)

## Built on by (most cited first, 1 of 1)

- [Flexible Selective Inference with Flow-based Transport Maps](https://mlsanity.com/paper/2506.01150/) (2025)

## Abstract (arXiv)

Conditional selective inference requires an exact characterization of the selection event, which is often unavailable except for a few examples like the lasso. This work addresses this challenge by introducing a generic approach to estimate the selection event, facilitating feasible inference conditioned on the selection event. The method proceeds by repeatedly generating bootstrap data and running the selection algorithm on the new datasets. Using the outputs of the selection algorithm, we can estimate the selection probability as a function of certain summary statistics. This leads to an estimate of the distribution of the data conditioned on the selection event, which forms the basis for conditional selective inference. We provide a theoretical guarantee assuming both asymptotic normality of relevant statistics and accurate estimation of the selection probability. The applicability of the proposed method is demonstrated through a variety of problems that lack exact characterizations of selection, where conditional selective inference was previously infeasible.