Dimension-independent learning rates for high-dimensional classification problems

2024/09/26 by Andres Felipe Lerma-Pineda, Lerma-Pineda, Andres Felipe, Philipp Petersen +5
Computer Science · #41A25 #41A46 #62C20 #68T05 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2409.17991

openalex publication_date 2024/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the problem of approximating and estimating classification functions that have their decision boundary in the RBV² space. Functions of RBV² type arise naturally as solutions of regularized neural network learning problems and neural networks can approximate these functions without the curse of dimensionality. We modify existing results to show that every RBV² function can be approximated by a neural network with bounded weights. Thereafter, we prove the existence of a neural network with bounded weights approximating a classification function. And we leverage these bounds to quantify the estimation rates. Finally, we present a numerical study that analyzes the effect of different regularity conditions on the decision boundaries.

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