# Data thinning for convolution-closed distributions

arXiv: https://arxiv.org/abs/2301.07276 · HTML: https://mlsanity.com/paper/2301.07276/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 47 references that are in the map.
- First posted on arXiv 18 Jan 2023.

## Builds on (most cited first, 8 of 8)

- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [Selective Inference for Hierarchical Clustering](https://mlsanity.com/paper/2012.02936/) (2020)
- [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)
- [Estimating the number of clusters using cross-validation](https://mlsanity.com/paper/1702.02658/) (2017)
- [Estimating Graph Dimension with Cross-validated Eigenvalues](https://mlsanity.com/paper/2108.03336/) (2021)
- [Unbiased Risk Estimation in the Normal Means Problem via Coupled Bootstrap Techniques](https://mlsanity.com/paper/2111.09447/) (2021)
- [Inference after latent variable estimation for single-cell RNA sequencing data](https://mlsanity.com/paper/2207.00554/) (2022)

## Built on by (most cited first, 13 of 13)

- [Generalized Data Thinning Using Sufficient Statistics](https://mlsanity.com/paper/2303.12931/) (2023)
- [Interpretable Machine Learning for Discovery: Statistical Challenges & Opportunities](https://mlsanity.com/paper/2308.01475/) (2023)
- [A Flexible Defense Against the Winner's Curse](https://mlsanity.com/paper/2411.18569/) (2024)
- [Decomposing Gaussians with Unknown Covariance](https://mlsanity.com/paper/2409.11497/) (2024)
- [LOBSTUR: A Local Bootstrap Framework for Tuning Unsupervised Representations in Graph Neural Networks](https://mlsanity.com/paper/2505.14867/) (2025)
- [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)
- [Robust Spatiotemporal Epidemic Modeling with Integrated Adaptive Outlier Detection](https://mlsanity.com/paper/2507.09380/) (2025)
- [Rate doubly robust estimation for weighted average treatment effects](https://mlsanity.com/paper/2509.14502/) (2025)
- [Integrating RCTs, RWD, AI/ML and Statistics: Next-Generation Evidence Synthesis](https://mlsanity.com/paper/2511.19735/) (2025)
- [Testing hypotheses via orthogonalization](https://mlsanity.com/paper/2606.29732/) (2026)
- [Physics-Driven Independent Pair Generation for Iterative Self-Supervised Low-Dose CT Denoising](https://mlsanity.com/paper/2609.02654/) (2026)
- [Selective Inference for Clustering Under Unknown Covariance](https://mlsanity.com/paper/2610.17458/) (2026)

## Abstract (arXiv)

We propose data thinning, an approach for splitting an observation into two or more independent parts that sum to the original observation, and that follow the same distribution as the original observation, up to a (known) scaling of a parameter. This very general proposal is applicable to any convolution-closed distribution, a class that includes the Gaussian, Poisson, negative binomial, gamma, and binomial distributions, among others. Data thinning has a number of applications to model selection, evaluation, and inference. For instance, cross-validation via data thinning provides an attractive alternative to the usual approach of cross-validation via sample splitting, especially in settings in which the latter is not applicable. In simulations and in an application to single-cell RNA-sequencing data, we show that data thinning can be used to validate the results of unsupervised learning approaches, such as k-means clustering and principal components analysis, for which traditional sample splitting is unattractive or unavailable.