# Data fission: splitting a single data point

arXiv: https://arxiv.org/abs/2112.11079 · HTML: https://mlsanity.com/paper/2112.11079/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 54 references that are in the map.
- First posted on arXiv 21 Dec 2021.

## Builds on (most cited first, 15 of 15)

- [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)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [Admissible anytime-valid sequential inference must rely on nonnegative martingales](https://mlsanity.com/paper/2009.03167/) (2020)
- [Adaptive piecewise polynomial estimation via trend filtering](https://mlsanity.com/paper/1304.2986/) (2013)
- [AdaPT: An interactive procedure for multiple testing with side information](https://mlsanity.com/paper/1609.06035/) (2016)
- [Splitting strategies for post-selection inference](https://mlsanity.com/paper/2102.02159/) (2021)
- [Fast and Flexible ADMM Algorithms for Trend Filtering](https://mlsanity.com/paper/1406.2082/) (2014)
- [Controlling False Discovery Rate Using Gaussian Mirrors](https://mlsanity.com/paper/1911.09761/) (2019)
- [Small sample methods for cluster-robust variance estimation and hypothesis testing in fixed effects models](https://mlsanity.com/paper/1601.01981/) (2016)
- [More powerful selective inference for the graph fused lasso](https://mlsanity.com/paper/2109.10451/) (2021)
- [Unbiased Risk Estimation in the Normal Means Problem via Coupled Bootstrap Techniques](https://mlsanity.com/paper/2111.09447/) (2021)
- [STAR: A general interactive framework for FDR control under structural constraints](https://mlsanity.com/paper/1710.02776/) (2017)
- [Empirical Bayes mean estimation with nonparametric errors via order statistic regression on replicated data](https://mlsanity.com/paper/1911.05970/) (2019)

## Built on by (most cited first, 14 of 14)

- [Data thinning for convolution-closed distributions](https://mlsanity.com/paper/2301.07276/) (2023)
- [Valid Inference After Causal Discovery](https://mlsanity.com/paper/2208.05949/) (2022)
- [Generalized Data Thinning Using Sufficient Statistics](https://mlsanity.com/paper/2303.12931/) (2023)
- [A Flexible Defense Against the Winner's Curse](https://mlsanity.com/paper/2411.18569/) (2024)
- [Self-Supervised Learning from Noisy and Incomplete Data](https://mlsanity.com/paper/2601.03244/) (2026)
- [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)
- [Causal Information Splitting: Engineering Proxy Features for Robustness to Distribution Shifts](https://mlsanity.com/paper/2305.05832/) (2023)
- [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)
- [Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurements](https://mlsanity.com/paper/2510.27663/) (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)

Suppose we observe a random vector X from some distribution P in a known family with unknown parameters. We ask the following question: when is it possible to split X into two parts f(X) and g(X) such that neither part is sufficient to reconstruct X by itself, but both together can recover X fully, and the joint distribution of (f(X),g(X)) is tractable? As one example, if X=(X1,dots,Xn) and P is a product distribution, then for any m<n, we can split the sample to define f(X)=(X1,dots,Xm) and g(X)=(Xm+1,dots,Xn). Rasines and Young (2022) offers an alternative approach that uses additive Gaussian noise -- this enables post-selection inference in finite samples for Gaussian distributed data and asymptotically when errors are non-Gaussian. In this paper, we offer a more general methodology for achieving such a split in finite samples by borrowing ideas from Bayesian inference to yield a (frequentist) solution that can be viewed as a continuous analog of data splitting. We call our method data fission, as an alternative to data splitting, data carving and p-value masking. We exemplify the method on a few prototypical applications, such as post-selection inference for trend filtering and other regression problems.