2010/09/29 by Gilles Blanchard, Blanchard, Gilles, Kraemer, Nicole · 3 citations
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Methodology (stat.ME) #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1009.5839
openalex publication_date 2010/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. The rates depend on two key quantities: first, on the regularity of the target regression function and second, on the intrinsic dimensionality of the data mapped into the kernel space. Lower bounds on attainable rates depending on these two quantities were established in earlier literature, and we obtain upper bounds for the considered method that match these lower bounds (up to a log factor) if the true regression function belongs to the reproducing kernel Hilbert space. If this assumption is not fulfilled, we obtain similar convergence rates provided additional unlabeled data are available. The order of the learning rates match state-of-the-art results that were recently obtained for least squares support vector machines and for linear regularization operators.