HARFE：硬岭随机特征展开
HARFE: Hard-Ridge Random Feature Expansion
AI总结：
本研究提出硬岭随机特征展开方法HARFE，结合硬阈值追踪算法与稀疏岭回归，采用随机稀疏连接模式匹配加性假设，证明收敛性且在实验中误差优于或持平于前沿算法。
摘要：
我们提出了一种用于逼近高维稀疏加性函数的随机特征模型，名为硬岭随机特征展开方法（HARFE）。该方法将基于硬阈值追踪的算法应用于稀疏岭回归（SRR）问题，以逼近随机特征矩阵对应的系数。SRR的公式在获取表示中使用更少项的稀疏模型，与往往对噪声和离群点具有鲁棒性的基于岭的平滑之间取得平衡。此外，我们在随机特征矩阵中采用随机稀疏连接模式，以匹配加性函数假设。我们证明，HARFE方法保证能够收敛，其误差界取决于噪声和稀疏岭回归模型的参数。基于合成数据以及真实数据集的数值结果，HARFE方法相比其他前沿算法取得了更低（或相当）的误差。
英文摘要：
We propose a random feature model for approximating high-dimensional sparse additive functions called the hard-ridge random feature expansion method (HARFE). This method utilizes a hard-thresholding pursuit-based algorithm applied to the sparse ridge regression (SRR) problem to approximate the coefficients with respect to the random feature matrix. The SRR formulation balances between obtaining sparse models that use fewer terms in their representation and ridge-based smoothing that tend to be robust to noise and outliers. In addition, we use a random sparse connectivity pattern in the random feature matrix to match the additive function assumption. We prove that the HARFE method is guaranteed to converge with a given error bound depending on the noise and the parameters of the sparse ridge regression model. Based on numerical results on synthetic data as well as on real datasets, the HARFE approach obtains lower (or comparable) error than other state-of-the-art algorithms.
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