Summary of Robust Sparse Estimation For Gaussians with Optimal Error Under Huber Contamination, by Ilias Diakonikolas et al.
Robust Sparse Estimation for Gaussians with Optimal Error under Huber Contamination
by Ilias Diakonikolas, Daniel M. Kane, Sushrut Karmalkar, Ankit Pensia, Thanasis Pittas
First submitted to arxiv on: 15 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Data Structures and Algorithms (cs.DS); Statistics Theory (math.ST); 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 paper proposes robust estimation methods for Gaussian sparse estimation tasks under Huber’s contamination model. The authors focus on mean estimation, principal component analysis (PCA), and linear regression, developing computationally efficient algorithms with optimal error guarantees within constant factors. These algorithms outperform prior efficient approaches in terms of quantifiable error. For example, the proposed algorithm for Gaussian robust k-sparse mean estimation achieves a sample complexity of O(k2/ε2) polylog(d/ε), running time that is polynomial in the sample size, and an ℓ_2-error of O(ε). In contrast, previous efficient algorithms inherently incur error Ω(ε√log(1/ε)). The authors also introduce a novel multidimensional filtering method that may have applications beyond this specific problem. This work contributes to the development of robust estimation methods for high-dimensional data. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper is about finding ways to accurately estimate things from noisy and possibly corrupted data. The researchers focus on three types of tasks: estimating the average value, identifying patterns in the data, and making predictions based on that data. They develop new algorithms that are both fast and accurate, outperforming previous methods. For example, one algorithm can estimate a mean value with an error of just O(ε), which is much better than what was possible before. The authors also introduce a new technique for filtering noisy data that may be useful in other areas. |
Keywords
* Artificial intelligence * Linear regression * Pca * Principal component analysis
