# Approximate Data Deletion in Generative Models

arXiv: https://arxiv.org/abs/2206.14439 · HTML: https://mlsanity.com/paper/2206.14439/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 29 Jun 2022.

## Builds on (most cited first, 28 of 28)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (2019)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [Approximate Data Deletion from Machine Learning Models](https://mlsanity.com/paper/2002.10077/) (2020)
- [Reconstructing Training Data with Informed Adversaries](https://mlsanity.com/paper/2201.04845/) (2022)
- [On the Accuracy of Influence Functions for Measuring Group Effects](https://mlsanity.com/paper/1905.13289/) (2019)
- [Machine Unlearning via Algorithmic Stability](https://mlsanity.com/paper/2102.13179/) (2021)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [On Second-Order Group Influence Functions for Black-Box Predictions](https://mlsanity.com/paper/1911.00418/) (2019)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [A Swiss Army Infinitesimal Jackknife](https://mlsanity.com/paper/1806.00550/) (2018)
- [Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation](https://mlsanity.com/paper/2006.06979/) (2020)
- [Featurized Density Ratio Estimation](https://mlsanity.com/paper/2107.02212/) (2021)
- [Understanding Instance-based Interpretability of Variational Auto-Encoders](https://mlsanity.com/paper/2105.14203/) (2021)
- [Training Neural Networks for Likelihood/Density Ratio Estimation](https://mlsanity.com/paper/1911.00405/) (2019)
- [A Higher-Order Swiss Army Infinitesimal Jackknife](https://mlsanity.com/paper/1907.12116/) (2019)
- [Sliding Window Algorithms for k-Clustering Problems](https://mlsanity.com/paper/2006.05850/) (2020)
- [The Inductive Bias of Restricted f-GANs](https://mlsanity.com/paper/1809.04542/) (2018)
- [Deep density ratio estimation for change point detection](https://mlsanity.com/paper/1905.09876/) (2019)
- [Towards GANs' Approximation Ability](https://mlsanity.com/paper/2004.05912/) (2020)

## Built on by (most cited first, 4 of 4)

- [Data Unlearning in Diffusion Models](https://mlsanity.com/paper/2503.01034/) (2025)
- [A Survey on Machine Unlearning: Techniques and New Emerged Privacy Risks](https://mlsanity.com/paper/2406.06186/) (2024)
- [Data Redaction from Conditional Generative Models](https://mlsanity.com/paper/2305.11351/) (2023)
- [Can Membership Inferencing be Refuted?](https://mlsanity.com/paper/2303.03648/) (2023)

## Abstract (arXiv)

Users have the right to have their data deleted by third-party learned systems, as codified by recent legislation such as the General Data Protection Regulation (GDPR) and the California Consumer Privacy Act (CCPA). Such data deletion can be accomplished by full re-training, but this incurs a high computational cost for modern machine learning models. To avoid this cost, many approximate data deletion methods have been developed for supervised learning. Unsupervised learning, in contrast, remains largely an open problem when it comes to (approximate or exact) efficient data deletion. In this paper, we propose a density-ratio-based framework for generative models. Using this framework, we introduce a fast method for approximate data deletion and a statistical test for estimating whether or not training points have been deleted. We provide theoretical guarantees under various learner assumptions and empirically demonstrate our methods across a variety of generative methods.