Summary of A Universal Growth Rate For Learning with Smooth Surrogate Losses, by Anqi Mao et al.
A Universal Growth Rate for Learning with Smooth Surrogate Losses
by Anqi Mao, Mehryar Mohri, Yutao Zhong
First submitted to arxiv on: 9 May 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 paper presents a comprehensive analysis of the growth rate of H-consistency bounds for various surrogate losses used in classification. The authors prove a square-root growth rate near zero for smooth margin-based surrogate losses in binary classification, providing both upper and lower bounds under mild assumptions. This result also translates to excess error bounds. The paper extends this analysis to multi-class classification with novel results, demonstrating a universal square-root growth rate for smooth comp-sum and constrained losses. The authors then examine how H-consistency bounds vary across surrogates based on the number of classes and identify minimizability gaps as the key differentiating factor in these bounds. This guides surrogate loss selection by comparing comp-sum losses, conditions where gaps become zero, and general conditions leading to small gaps. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how fast the error rate decreases when using different surrogates for classification problems. They show that some surrogates are much better than others in certain situations, especially when there are many classes. The authors also find that some surrogates have big “gaps” in their performance, which can help us choose the best one to use. |
Keywords
» Artificial intelligence » Classification
