Summary of Statistical and Topological Properties Of Gaussian Smoothed Sliced Probability Divergences, by Alain Rakotomamonjy et al.
Statistical and Topological Properties of Gaussian Smoothed Sliced Probability Divergences
by Alain Rakotomamonjy, Mokhtar Z. Alaya, Maxime Berar, Gilles Gasso
First submitted to arxiv on: 20 Oct 2021
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Cryptography and Security (cs.CR)
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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 This paper explores the theoretical properties of Gaussian smoothed sliced Wasserstein distance, a metric for comparing probability distributions while preserving privacy. The authors analyze the computational and statistical properties of this distance and its generalized versions, showing that smoothing and slicing preserve the metric property and weak topology. They also investigate the sample complexity of these divergences and examine how the amount of Gaussian smoothing affects the divergence’s privacy level. Empirical studies demonstrate the effectiveness of these distances in privacy-preserving domain adaptation. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at a special way to measure how similar two sets of numbers are, while keeping the numbers private. The method is called Gaussian smoothed sliced Wasserstein distance. It’s used in things like adapting data from one place to another without giving away any secrets. The researchers studied this method and found out what makes it work well or not so well. They also tested it with real data and showed that it can be very good at keeping information private while still getting useful results. |
Keywords
* Artificial intelligence * Domain adaptation * Probability
