Summary of Stochastic Gradient Descent For Nonparametric Regression, by Xin Chen and Jason M. Klusowski
Stochastic Gradient Descent for Nonparametric Regression
by Xin Chen, Jason M. Klusowski
First submitted to arxiv on: 1 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 The paper presents an iterative algorithm for training nonparametric additive models that has more favorable memory storage and computational requirements compared to existing methods. The algorithm can be seen as the functional counterpart of stochastic gradient descent, applied to the coefficients of a truncated basis expansion of the component functions. The resulting estimator satisfies an oracle inequality that allows for model mis-specification. In the well-specified setting, by choosing the learning rate carefully across three distinct stages of training, the paper demonstrates that its risk is minimax optimal in terms of the dependence on the dimensionality of the data and the size of the training sample. Additionally, polynomial convergence rates are provided even when the covariates do not have full support on their domain. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper develops a new algorithm for training models that can be used to analyze complex data sets. The algorithm is special because it’s efficient in terms of how much memory and computing power it needs. It works by adjusting the coefficients of a set of basic functions to fit the data. This algorithm has an important property called an “oracle inequality” which means it can still work well even if the model isn’t perfect. In the best-case scenario, this algorithm’s performance is optimal given the amount of data and information available. |
Keywords
* Artificial intelligence * Stochastic gradient descent
