The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques based on sparse spectrum Gaussian processes, we focus on models given by regularized trigonometric linear regression. This paper provides an analysis of the performance of such an estimation set-up within the statistical learning framework. In particular, we derive a novel bound for the sample error in finite-dimensional spaces, accounting for noise with potentially unbounded support. Next, we study the approximation error and discuss the bias-variance trade-off as a function of the regularization parameter by combining the two bounds.

翻译：非参数化、基于核方法的函数估计有效性是以高昂计算复杂度为代价的，这限制了其在自适应、基于模型的控制中的适用性。受基于稀疏谱高斯过程的逼近技术启发，本文聚焦于由正则化三角函数线性回归给出的模型。本文在统计学习框架下分析了此类估计方法的性能。具体地，我们推导了有限维空间中样本误差的一个新边界，该边界考虑了潜在无界支撑的噪声。接着，我们研究了逼近误差，并通过结合两个边界讨论了正则化参数对偏差-方差权衡的影响。