Summary of Computational-statistical Gaps For Improper Learning in Sparse Linear Regression, by Rares-darius Buhai et al.
Computational-Statistical Gaps for Improper Learning in Sparse Linear Regression
by Rares-Darius Buhai, Jingqiu Ding, Stefan Tiegel
First submitted to arxiv on: 21 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computational Complexity (cs.CC); 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 proposed research investigates the computational-statistical gaps for improper learning in sparse linear regression. In essence, it explores the minimum sample complexity required to efficiently find a potentially dense estimate for the regression vector that achieves non-trivial prediction error on the given samples. The study reveals that information-theoretically, this can be achieved using θ(k log (d/k)) samples. However, there is currently no known polynomial-time algorithm that achieves the same guarantees using fewer than θ(d) samples without additional restrictions on the model. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at how to learn from data when we don’t know what the important features are. It’s like trying to find a treasure map in a big pile of junk, where some pieces might be clues and others aren’t. The researchers want to know how many samples (pieces of treasure) they need to collect before they can make a good guess about which pieces are actually part of the map. They found that it takes θ(k log (d/k)) samples to get a good estimate, but there isn’t an efficient way to do it with fewer than θ(d) samples without some extra rules. |
Keywords
* Artificial intelligence * Linear regression * Regression
