2012/03/20 by Robert Hable, Hable, Robert · 1 citation
Engineering · Mathematics · #62G08 #62G15 #FOS: Computer and information sciences #Machine Learning (stat.ML) #Mathematical Approximation and Integration #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1203.4354
openalex publication_date 2012/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Regularized kernel methods such as, e.g., support vector machines and\nleast-squares support vector regression constitute an important class of\nstandard learning algorithms in machine learning. Theoretical investigations\nconcerning asymptotic properties have manly focused on rates of convergence\nduring the last years but there are only very few and limited (asymptotic)\nresults on statistical inference so far. As this is a serious limitation for\ntheir use in mathematical statistics, the goal of the article is to fill this\ngap. Based on asymptotic normality of many of these methods, the article\nderives a strongly consistent estimator for the unknown covariance matrix of\nthe limiting normal distribution. In this way, we obtain asymptotically correct\nconfidence sets for \ψ(fP,\λ0) where fP,\λ0 denotes the\nminimizer of the regularized risk in the reproducing kernel Hilbert space H\nand \ψ:H\→ mathdsRm is any Hadamard-differentiable functional.\nApplications include (multivariate) pointwise confidence sets for values of\nfP,\λ0 and confidence sets for gradients, integrals, and norms.\n