# Anonymous Learning via Look-Alike Clustering: A Precise Analysis of Model Generalization

arXiv: https://arxiv.org/abs/2310.04015 · HTML: https://mlsanity.com/paper/2310.04015/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 6 Oct 2023.

## Builds on (most cited first, 17 of 17)

- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [Just Interpolate: Kernel "Ridgeless" Regression Can Generalize](https://mlsanity.com/paper/1808.00387/) (2018)
- [To understand deep learning we need to understand kernel learning](https://mlsanity.com/paper/1802.01396/) (2018)
- [When is Memorization of Irrelevant Training Data Necessary for High-Accuracy Learning?](https://mlsanity.com/paper/2012.06421/) (2020)
- [A Model of Double Descent for High-dimensional Binary Linear Classification](https://mlsanity.com/paper/1911.05822/) (2019)
- [Precise Tradeoffs in Adversarial Training for Linear Regression](https://mlsanity.com/paper/2002.10477/) (2020)
- [Overlearning Reveals Sensitive Attributes](https://mlsanity.com/paper/1905.11742/) (2019)
- [Precise Statistical Analysis of Classification Accuracies for Adversarial Training](https://mlsanity.com/paper/2010.11213/) (2020)
- [Explaining the Success of AdaBoost and Random Forests as Interpolating Classifiers](https://mlsanity.com/paper/1504.07676/) (2015)
- [The curse of overparametrization in adversarial training: Precise analysis of robust generalization for random features regression](https://mlsanity.com/paper/2201.05149/) (2022)
- [Identity Crisis: Memorization and Generalization under Extreme Overparameterization](https://mlsanity.com/paper/1902.04698/) (2019)
- [Honest-but-Curious Nets: Sensitive Attributes of Private Inputs Can Be Secretly Coded into the Classifiers' Outputs](https://mlsanity.com/paper/2105.12049/) (2021)
- [Massively Parallel and Dynamic Algorithms for Minimum Size Clustering](https://mlsanity.com/paper/2106.02685/) (2021)
- [Capacitated Center Problems with Two-Sided Bounds and Outliers](https://mlsanity.com/paper/1702.07435/) (2017)

## Built on by (most cited first, 2 of 2)

- [Modeling Churn in Recommender Systems with Aggregated Preferences](https://mlsanity.com/paper/2502.18483/) (2025)
- [Churn-Aware Recommendation Planning under Aggregated Preference Feedback](https://mlsanity.com/paper/2507.04513/) (2025)

## Abstract (arXiv)

While personalized recommendations systems have become increasingly popular, ensuring user data protection remains a top concern in the development of these learning systems. A common approach to enhancing privacy involves training models using anonymous data rather than individual data. In this paper, we explore a natural technique called look-alike clustering, which involves replacing sensitive features of individuals with the cluster's average values. We provide a precise analysis of how training models using anonymous cluster centers affects their generalization capabilities. We focus on an asymptotic regime where the size of the training set grows in proportion to the features dimension. Our analysis is based on the Convex Gaussian Minimax Theorem (CGMT) and allows us to theoretically understand the role of different model components on the generalization error. In addition, we demonstrate that in certain high-dimensional regimes, training over anonymous cluster centers acts as a regularization and improves generalization error of the trained models. Finally, we corroborate our asymptotic theory with finite-sample numerical experiments where we observe a perfect match when the sample size is only of order of a few hundreds.