有界噪声下基于核的学习技术的确定性误差界
Deterministic error bounds for kernel-based learning techniques under bounded noise
摘要：
我们考虑的问题，重建一个函数从一个有限的噪声损坏的样本。分析了核岭回归和$\varepsilon$ -支持向量回归两种核算法。通过假设地面真值函数属于所选核的再生核Hilbert空间，并且影响数据集的测量噪声是有界的，我们采用近似理论的观点建立了两个模型的有限样本误差界\textit{deterministic}。最后，我们讨论了它们与高斯过程的关系，并给出了两个数值例子。在建立我们的不等式，我们希望能够帮助使非参数核学习和系统辨识领域的鲁棒控制更接近对方。
英文摘要：
We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and $\varepsilon$-support vector regression. By assuming the ground-truth function belongs to the reproducing kernel Hilbert space of the chosen kernel, and the measurement noise affecting the dataset is bounded, we adopt an approximation theory viewpoint to establish \textit{deterministic}, finite-sample error bounds for the two models. Finally, we discuss their connection with Gaussian processes and two numerical examples are provided. In establishing our inequalities, we hope to help bring the fields of non-parametric kernel learning and system identification for robust control closer to each other.
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