Summary of Dimension-free Private Mean Estimation For Anisotropic Distributions, by Yuval Dagan et al.
Dimension-free Private Mean Estimation for Anisotropic Distributions
by Yuval Dagan, Michael I. Jordan, Xuelin Yang, Lydia Zakynthinou, Nikita Zhivotovskiy
First submitted to arxiv on: 1 Nov 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed algorithms for high-dimensional mean estimation achieve differential privacy while avoiding the curse of dimensionality. By developing estimators that are suitable for anisotropic subgaussian distributions, the authors demonstrate improved sample complexity that is independent of the dimension. The presented estimator achieves error |-|_2 with a bound that does not depend on the dimension when the signal is concentrated in a few principal components. Furthermore, the optimal sample complexity for this task up to logarithmic factors is established. Additionally, an algorithm is presented whose sample complexity has improved dependence on the dimension, from d^{1/2} to d^{1/4}. The proposed methods have potential applications in machine learning and data analysis. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper presents new ways to estimate the mean of a dataset while keeping it private. This is important because sometimes we want to keep certain information about a dataset secret, but still be able to use it for important tasks like finding averages or patterns. The authors show that their methods can work well even when dealing with large amounts of data and many features (like images). They also compare their results to other methods and find that they are the best up to a certain point. |
Keywords
* Artificial intelligence * Machine learning
