用迭代加权核方法高效学习稀疏函数，揭示了核方法也能捕捉数据的低维结构。
Iteratively reweighted kernel machines efficiently learn sparse functions
- 通过导数检测重要特征坐标，实现低样本复杂度识别
- 迭代加权重训练使核机在有限步内高效学习分层多项式
- 适合研究模型可解释性与稀疏学习的学者参考
神经网络出色的实践表现常归因于其能从数据中直接学习低维表示和分层结构。本文认为这两种现象并非神经网络独有，经典核方法同样具备。我们证明核预测器的导数可在低样本复杂度下识别关键坐标；通过迭代利用导数对数据加权并重训练核机，可高效学习分层多项式，且具有有限跳跃复杂度。数值实验验证了理论结果。
原文摘要 · Abstract (English)
The impressive practical performance of neural networks is often attributed to their ability to learn low-dimensional data representations and hierarchical structure directly from data. In this work, we argue that these two phenomena are not unique to neural networks, and can be elicited from classical kernel methods. Namely, we show that the derivative of the kernel predictor can detect the influential coordinates with low sample complexity. Moreover, by iteratively using the derivatives to reweight the data and retrain kernel machines, one is able to efficiently learn hierarchical polynomials with finite leap complexity. Numerical experiments illustrate the developed theory.
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