论文检索

函数型图形套索AI 解读

We consider the problem of recovering conditional independence relationships between p jointly distributed Hilbertian random elements given n realizations thereof. We operate in the sparse high-dimensional regime, where n ≪ p and no element is related to more than d ≪ p other elements. In this context, we propose an infinite-dimensional generalization of the graphical lasso. We prove model selection consistency under natural assumptions and extend many classical results to…

协方差核的补全AI 解读

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Ω of a rectangular domain I×I to a covariance kernel on the entire domain I×I. For a broad class of domains Ω called serrated domains, we are able to present a complete theory. Namely, we demonstrate that a canonical completion always exists and can be explicitly constructed. We characterise all possible completions as suitable perturbations of…