用小波特征实现高效非平稳核近似，兼具精度与速度。
Scalable Random Wavelet Features: Efficient Non-Stationary Kernel Approximation with Convergence Guarantees
- 通过采样小波族构造显式特征映射，捕捉输入依赖的复杂模式。
- 在多个真实和合成数据集上优于传统随机特征方法，性能接近复杂模型。
- 理论保证完备，适合需要高表达力又追求计算效率的研究者。
建模统计特性随输入域变化的非平稳过程是机器学习中的关键挑战；然而大多数可扩展方法依赖平稳性假设。这导致两难选择：使用表达力强但计算代价高的深度高斯过程，或使用可扩展但受限的随机傅里叶特征（RFF）。本文提出随机小波特征（RWF），通过从小波族中采样构建可扩展的非平稳核近似。利用小波的局部化与多分辨率结构，RWF生成能捕捉复杂输入依赖模式的显式特征映射。该框架为RFF向非平稳场景的推广提供了理论基础，并具备正定性、无偏性及一致收敛性等完整理论分析。在多个具有挑战性的合成与真实世界数据集上，RWF表现优于平稳随机特征，且在准确率与效率间达到良好平衡，使可扩展且富有表现力的核方法适用于广泛的非平稳实际问题。
原文摘要 · Abstract (English)
Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult trade-off: use expressive but computationally demanding models like Deep Gaussian Processes, or scalable but limited methods like Random Fourier Features (RFF). We close this gap by introducing Random Wavelet Features (RWF), a framework that constructs scalable, non-stationary kernel approximations by sampling from wavelet families. By harnessing the inherent localization and multi-resolution structure of wavelets, RWF generates an explicit feature map that captures complex, input-dependent patterns. Our framework provides a principled way to generalize RFF to the non-stationary setting and comes with a comprehensive theoretical analysis, including positive definiteness, unbiasedness, and uniform convergence guarantees. We demonstrate empirically on a range of challenging synthetic and real-world datasets that RWF outperforms stationary random features and offers a compelling accuracy-efficiency trade-off against more complex models, unlocking scalable and expressive kernel methods for a broad class of real-world non-stationary problems.
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