Summary of Overfitting Behaviour Of Gaussian Kernel Ridgeless Regression: Varying Bandwidth or Dimensionality, by Marko Medvedev et al.
Overfitting Behaviour of Gaussian Kernel Ridgeless Regression: Varying Bandwidth or Dimensionality
by Marko Medvedev, Gal Vardi, Nathan Srebro
First submitted to arxiv on: 5 Sep 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 investigates the overfitting behavior of minimum norm interpolating solutions in Gaussian kernel ridge regression, specifically when the bandwidth or input dimension changes with sample size. The authors show that even with tuning or varying bandwidths, the ridgeless solution is never consistent and often performs worse than a null predictor for large enough noise levels. As the input dimension increases, the paper provides a characterization of overfitting behavior using sub-polynomial scaling dimensions. The study finds benign overfitting in Gaussian kernel regression with sub-polynomial scaling. All results rely on the Gaussian universality ansatz and risk predictions based on kernel eigenstructure. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how well machine learning models do when they’re asked to make predictions about data that’s very different from what they were trained on. They find that even if you adjust the model to fit the new data better, it can still make poor choices. The researchers also figure out why this happens and show that sometimes, surprisingly, this kind of overfitting can actually be helpful. They use special math tools called kernel eigenstructure to understand how well their models are doing. |
Keywords
» Artificial intelligence » Machine learning » Overfitting » Regression
