Summary of Learning Orthogonal Multi-index Models: a Fine-grained Information Exponent Analysis, by Yunwei Ren et al.
Learning Orthogonal Multi-Index Models: A Fine-Grained Information Exponent Analysis
by Yunwei Ren, Jason D. Lee
First submitted to arxiv on: 13 Oct 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 This paper explores the role of information exponent in predicting the sample complexity of online stochastic gradient descent (SGD) for multi-index Gaussian models. Building upon previous work by Ben Arous et al. [2021], which introduced the concept of information exponent as equivalent to the lowest degree in Hermite expansion of link functions for single-index Gaussian models, this study highlights the limitations of focusing solely on the lowest degree when dealing with multi-index models. The authors demonstrate that neglecting higher-degree terms can lead to suboptimal rates and emphasize the importance of considering structural details in model design. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about how we can improve a type of machine learning algorithm called online stochastic gradient descent (SGD). Previously, researchers introduced an important concept called information exponent, which helps us understand how well SGD works for simple models. In this new study, the authors show that when dealing with more complex models, just using this simple idea isn’t enough. They demonstrate that we need to consider more details about the model to get the best results. |
Keywords
» Artificial intelligence » Machine learning » Stochastic gradient descent
