Summary of Cryptographic Hardness Of Score Estimation, by Min Jae Song
Cryptographic Hardness of Score Estimation
by Min Jae Song
First submitted to arxiv on: 4 Apr 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computational Complexity (cs.CC); Cryptography and Security (cs.CR); 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 This paper demonstrates that estimating scores accurately in a dataset without assuming strong knowledge about the data distribution is computationally challenging, even when the sample size grows polynomially with relevant problem parameters. The authors build upon previous work by Chen et al. (ICLR 2023), which showed that generating samples from an unknown distribution is equivalent to accurate score estimation. The study focuses on “Gaussian pancakes” distributions, originally proposed by Diakonikolas et al. (FOCS 2017), and proves their computational indistinguishability from standard Gaussian distributions under widely accepted assumptions in lattice-based cryptography (Bruna et al., STOC 2021; Gupte et al., FOCS 2022). This work has implications for understanding the limits of machine learning algorithms and highlights the importance of careful assumption-making. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper shows that it’s hard to accurately estimate scores in a dataset without making strong assumptions about the data. Even if we have lots of samples, it’s still difficult. The authors use a special type of distribution called “Gaussian pancakes” to prove this point. These distributions are tricky to work with and are similar to standard Gaussian distributions in many ways. This research helps us understand what machine learning algorithms can do and how they should be used. |
Keywords
* Artificial intelligence * Machine learning
