Summary of Semi-supervised Deep Sobolev Regression: Estimation and Variable Selection by Requ Neural Network, By Zhao Ding and Chenguang Duan and Yuling Jiao and Jerry Zhijian Yang
Semi-Supervised Deep Sobolev Regression: Estimation and Variable Selection by ReQU Neural Network
by Zhao Ding, Chenguang Duan, Yuling Jiao, Jerry Zhijian Yang
First submitted to arxiv on: 9 Jan 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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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 Semi-supervised Deep Sobolev Regressor (SDORE) is a novel approach for estimating underlying regression functions and their gradients without assuming a specific parametric form. This method uses deep ReQU neural networks to minimize empirical risk with gradient norm regularization, allowing the approximation of the regularization term using unlabeled data. Theoretical analysis shows that SDORE achieves minimax optimality in L2-norm convergence rates and provides insights for selecting regularization parameters and determining neural network size. Additionally, it offers a provable advantage in semi-supervised learning by leveraging unlabeled data. This approach has diverse applications, including nonparametric variable selection. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary SDORE is a new way to understand how things are related without knowing what the relationships look like ahead of time. It’s like trying to figure out what makes two things similar or different without having any specific rules to follow. SDORE uses special computers called neural networks and some clever math to make good guesses about these relationships, even when we don’t have a lot of information to work with. This is important because it can help us understand lots of different things, like what makes people similar or different, or how plants grow in different environments. |
Keywords
* Artificial intelligence * Neural network * Regression * Regularization * Semi supervised
