# Generalized Data Thinning Using Sufficient Statistics

arXiv: https://arxiv.org/abs/2303.12931 · HTML: https://mlsanity.com/paper/2303.12931/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 61 references that are in the map.
- First posted on arXiv 22 Mar 2023.

## Builds on (most cited first, 14 of 14)

- [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)
- [Veridical Data Science](https://mlsanity.com/paper/1901.08152/) (2019)
- [Selective Inference for Hierarchical Clustering](https://mlsanity.com/paper/2012.02936/) (2020)
- [Valid Inference Corrected for Outlier Removal](https://mlsanity.com/paper/1711.10635/) (2017)
- [Testing for a Change in Mean After Changepoint Detection](https://mlsanity.com/paper/1910.04291/) (2019)
- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [Post-Selection Inference for Changepoint Detection Algorithms with Application to Copy Number Variation Data](https://mlsanity.com/paper/1812.03644/) (2018)
- [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)
- [Unbiased Risk Estimation in the Normal Means Problem via Coupled Bootstrap Techniques](https://mlsanity.com/paper/2111.09447/) (2021)
- [Selective inference for clustering with unknown variance](https://mlsanity.com/paper/2301.12999/) (2023)
- [Inference after latent variable estimation for single-cell RNA sequencing data](https://mlsanity.com/paper/2207.00554/) (2022)

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

- [Selective inference using randomized group lasso estimators for general models](https://mlsanity.com/paper/2306.13829/) (2023)
- [Decomposing Gaussians with Unknown Covariance](https://mlsanity.com/paper/2409.11497/) (2024)
- [Statistical testing on generative AI anomaly detection tools in Alzheimer's Disease diagnosis](https://mlsanity.com/paper/2410.13363/) (2024)
- [Thinning a Wishart Random Matrix](https://mlsanity.com/paper/2502.09957/) (2025)
- [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)
- [Testing hypotheses via orthogonalization](https://mlsanity.com/paper/2606.29732/) (2026)
- [Selective Inference for Clustering Under Unknown Covariance](https://mlsanity.com/paper/2610.17458/) (2026)

## Abstract (arXiv)

Our goal is to develop a general strategy to decompose a random variable X into multiple independent random variables, without sacrificing any information about unknown parameters. A recent paper showed that for some well-known natural exponential families, X can be "thinned" into independent random variables X(1), ldots, X(K), such that X = sumk=1K X(k). These independent random variables can then be used for various model validation and inference tasks, including in contexts where traditional sample splitting fails. In this paper, we generalize their procedure by relaxing this summation requirement and simply asking that some known function of the independent random variables exactly reconstruct X. This generalization of the procedure serves two purposes. First, it greatly expands the families of distributions for which thinning can be performed. Second, it unifies sample splitting and data thinning, which on the surface seem to be very different, as applications of the same principle. This shared principle is sufficiency. We use this insight to perform generalized thinning operations for a diverse set of families.