# Flexible Selective Inference with Flow-based Transport Maps

arXiv: https://arxiv.org/abs/2506.01150 · HTML: https://mlsanity.com/paper/2506.01150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 44 references that are in the map.
- First posted on arXiv 1 Jun 2025.

## Builds on (most cited first, 27 of 27)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [Selective Inference for Hierarchical Clustering](https://mlsanity.com/paper/2012.02936/) (2020)
- [Bayesian Synthetic Likelihood](https://mlsanity.com/paper/2305.05120/) (2023)
- [More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming](https://mlsanity.com/paper/2105.04920/) (2021)
- [Splitting strategies for post-selection inference](https://mlsanity.com/paper/2102.02159/) (2021)
- [Data fission: splitting a single data point](https://mlsanity.com/paper/2112.11079/) (2021)
- [Data thinning for convolution-closed distributions](https://mlsanity.com/paper/2301.07276/) (2023)
- [Approximate selective inference via maximum likelihood](https://mlsanity.com/paper/1902.07884/) (2019)
- [Generalized Data Thinning Using Sufficient Statistics](https://mlsanity.com/paper/2303.12931/) (2023)
- [Simulation-based, Finite-sample Inference for Privatized Data](https://mlsanity.com/paper/2303.05328/) (2023)
- [Exact Selective Inference with Randomization](https://mlsanity.com/paper/2212.12940/) (2022)
- [Approximate Post-Selective Inference for Regression with the Group LASSO](https://mlsanity.com/paper/2012.15664/) (2020)
- [Repro Samples Method for Finite- and Large-Sample Inferences](https://mlsanity.com/paper/2206.06421/) (2022)
- [Locally Simultaneous Inference](https://mlsanity.com/paper/2212.09009/) (2022)
- [Selective inference using randomized group lasso estimators for general models](https://mlsanity.com/paper/2306.13829/) (2023)
- [Inference on the proportion of variance explained in principal component analysis](https://mlsanity.com/paper/2402.16725/) (2024)
- [An Exact Sampler for Inference after Polyhedral Model Selection](https://mlsanity.com/paper/2308.10346/) (2023)
- [Cross-Validation with Antithetic Gaussian Randomization](https://mlsanity.com/paper/2412.14423/) (2024)
- [Inference with Randomized Regression Trees](https://mlsanity.com/paper/2412.20535/) (2024)
- [Black-box Selective Inference via Bootstrapping](https://mlsanity.com/paper/2203.14504/) (2022)
- [Selective Inference in Graphical Models via Maximum Likelihood](https://mlsanity.com/paper/2503.24311/) (2025)

## Abstract (arXiv)

Data-carving methods perform selective inference by conditioning the distribution of data on the observed selection event. However, existing data-carving approaches typically require an analytically tractable characterization of the selection event. This paper introduces a new method that leverages tools from flow-based generative modeling to approximate a potentially complex conditional distribution, even when the underlying selection event lacks an analytical description -- take, for example, the data-adaptive tuning of model parameters. The key idea is to learn a transport map that pushes forward a simple reference distribution to the conditional distribution given selection. This map is efficiently learned via a normalizing flow, without imposing any further restrictions on the nature of the selection event. Through extensive numerical experiments on both simulated and real data, we demonstrate that this method enables flexible selective inference by providing: (i) valid p-values and confidence sets for adaptively selected hypotheses and parameters, (ii) a closed-form expression for the conditional density function, enabling likelihood-based and quantile-based inference, and (iii) adjustments for intractable selection steps that can be easily integrated with existing methods designed to account for the tractable steps in a selection procedure involving multiple steps.