提出高维分类中无需维度依赖的学习率，突破传统瓶颈。
Dimension-independent learning rates for high-dimensional classification problems
- 用有界权重的神经网络逼近RBV²类分类函数
- 证明了高维下估计误差率不随维度增长而恶化
- 适合研究高维机器学习泛化性能的学者
我们研究在RBV²空间中具有决策边界的分类函数的逼近与估计问题。此类函数自然出现在正则化神经网络学习中，且神经网络可无维度灾难地进行逼近。本文修正已有结果，证明任意RBV²函数均可由权重有界的神经网络逼近；进一步证明存在权重有界的神经网络可逼近分类函数，并据此量化估计速率。最后通过数值实验分析不同正则性条件对决策边界的影响。
原文摘要 · Abstract (English)
We study the problem of approximating and estimating classification functions that have their decision boundary in the $RBV^2$ space. Functions of $RBV^2$ 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 $RBV^2$ 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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