In this paper, we discuss the convergence analysis of the conjugate gradient-based algorithm for the functional linear model in the reproducing kernel Hilbert space framework, utilizing early stopping results in regularization against over-fitting. We establish the convergence rates depending on the regularity condition of the slope function and the decay rate of the eigenvalues of the operator composition of covariance and kernel operator. Our convergence rates match the minimax rate available from the literature.

翻译：本文在再生核希尔伯特空间框架下，讨论了基于共轭梯度的算法在函数线性模型中的收敛性分析，利用早期停止结果进行正则化以防止过拟合。我们建立了依赖于斜率函数正则性条件以及协方差与核算子复合算子特征值衰减率的收敛速率。该收敛速率与文献中可用的极小化最优速率相匹配。