# Statistical Unlearning of Distributions: A Hypothesis Testing Approach

arXiv: https://arxiv.org/abs/2605.16645 · HTML: https://mlsanity.com/paper/2605.16645/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 15 May 2026.

## Placed in

- LLM safety and security / [Machine unlearning](https://mlsanity.com/safety/machine-unlearning/)

## Builds on (most cited first, 24 of 24)

- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Learning the Difference that Makes a Difference with Counterfactually-Augmented Data](https://mlsanity.com/paper/1909.12434/) (2019)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Who's Harry Potter? Approximate Unlearning in LLMs](https://mlsanity.com/paper/2310.02238/) (2023)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [Towards Unbounded Machine Unlearning](https://mlsanity.com/paper/2302.09880/) (2023)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [Approximate Data Deletion from Machine Learning Models](https://mlsanity.com/paper/2002.10077/) (2020)
- [Fast Yet Effective Machine Unlearning](https://mlsanity.com/paper/2111.08947/) (2021)
- [Adversarial Removal of Demographic Attributes from Text Data](https://mlsanity.com/paper/1808.06640/) (2018)
- [Autoencoding Variational Inference For Topic Models](https://mlsanity.com/paper/1703.01488/) (2017)
- [Forget Unlearning: Towards True Data-Deletion in Machine Learning](https://mlsanity.com/paper/2210.08911/) (2022)
- [Langevin Unlearning: A New Perspective of Noisy Gradient Descent for Machine Unlearning](https://mlsanity.com/paper/2401.10371/) (2024)
- [Towards Certified Unlearning for Deep Neural Networks](https://mlsanity.com/paper/2408.00920/) (2024)
- [Certified Unlearning for Neural Networks](https://mlsanity.com/paper/2506.06985/) (2025)
- [Deep Unlearning: Fast and Efficient Gradient-free Approach to Class Forgetting](https://mlsanity.com/paper/2312.00761/) (2023)
- [Language Models May Verbatim Complete Text They Were Not Explicitly Trained On](https://mlsanity.com/paper/2503.17514/) (2025)
- [The Utility and Complexity of in- and out-of-Distribution Machine Unlearning](https://mlsanity.com/paper/2412.09119/) (2024)
- [When to Forget? Complexity Trade-offs in Machine Unlearning](https://mlsanity.com/paper/2502.17323/) (2025)
- [Finite-Sample Maximum Likelihood Estimation of Location](https://mlsanity.com/paper/2206.02348/) (2022)
- [Gaussian Certified Unlearning in High Dimensions: A Hypothesis Testing Approach](https://mlsanity.com/paper/2510.13094/) (2025)
- [Distributional Machine Unlearning via Selective Data Removal](https://mlsanity.com/paper/2507.15112/) (2025)

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

- [Certified Mechanistic Edits: Behavioral Guarantees for Skill Removal and Preservation](https://mlsanity.com/paper/2610.03502/) (2026)

## Abstract (arXiv)

Machine learning systems increasingly face requirements to forget not only individual data points, but entire domains of information, such as toxic language, copyrighted corpora, or demographic biases. This raises a fundamental dilemma of statistical-computational tradeoffs: removing all samples from an unwanted domain may be computationally prohibitive, while randomly removing a subset may not provide distribution-level statistical guarantees. We propose a statistical framework for distributional unlearning, in which domains are modeled as probability distributions, and the goal is to remove a carefully chosen subset of samples that reduces the effect of an unwanted distribution while preserving performance on a desired one. We formalize this using a hypothesis test of the edited data with the desired and unwanted domains, leading to an interpretable and robust criterion for selecting samples to remove. Within this statistical framework, we characterize the fundamental region of the allowable edited data distributions and the removal-preservation Pareto frontier for a broad class of distribution families. This includes parametric families such as shifted Gaussians of arbitrary dimension, a one-dimensional location family with log-concave noise, and the one-dimensional Poisson family. It also includes nonparametric families such as the Gaussian white noise model, a canonical model for nonparametric regression. We prove composition rules that describe how distributional unlearning behaves across multimodal unwanted domains, and introduce a central-limit behavior for the removal-preservation baselines when composing a large number of such families. Finally, we provide finite sample guarantees by providing Pareto frontiers for some selection algorithms, and observe an information-computation gap.