Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more
Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more
Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more
Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more
The evolutionary history of species may be described by a phylogenetic tree whose topology captures ancestral relationships among the species, and whose branch lengths denote evolution times. For a fixed topology and an assumed probabilistic model of nucleotide substitution, we show that the likelihood of a given tree is a d.c. (difference of convex) function … Read more
Density estimation is a classical and important problem in statistics. The aim of this paper is to develop a new computational approach to density estimation based on semidefinite programming (SDP), a new technology developed in optimization in the last decade. We express a density as the product of a nonnegative polynomial and a base density … Read more