Summary of Dimension-independent Learning Rates For High-dimensional Classification Problems, by Andres Felipe Lerma-pineda et al.
Dimension-independent learning rates for high-dimensional classification problems
by Andres Felipe Lerma-Pineda, Philipp Petersen, Simon Frieder, Thomas Lukasiewicz
First submitted to arxiv on: 26 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA); 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 investigates the approximation and estimation of classification functions whose decision boundary lies in the RBV^2 space. Neural networks can effectively approximate these functions without suffering from the curse of dimensionality, as they naturally arise as solutions to regularized neural network learning problems. The authors modify existing results to demonstrate that every RBV^2 function can be approximated by a neural network with bounded weights. Building on this foundation, they prove the existence of a neural network with bounded weights that can approximate a classification function. To further quantify estimation rates, the authors leverage these bounds. Finally, a numerical study is presented to analyze the impact of different regularity conditions on decision boundaries. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at ways to get computers to make good choices when they’re not sure what’s going on. They want to know how well neural networks can do this without getting overwhelmed by too much information. The authors show that these networks can actually do a great job of making decisions even when there’s a lot to consider, and they figure out ways to measure just how well they’re doing. Finally, they test their ideas with some computer experiments. |
Keywords
* Artificial intelligence * Classification * Neural network
