maximum likelihood estimation

Maximum Likelihood Probability Measures over Sets and Applications to Data-Driven Optimization

  • Juan Borrero
  • Denis Saure
    • Categories Applications - OR and Management Sciences, Optimization in Data Science, Robust Optimization Tags , ,

    Motivated by data-driven approaches to sequential decision-making under uncertainty, we study maximum likelihood estimation of a distribution over a general measurable space when, unlike traditional setups, realizations of the underlying uncertainty are not directly observable but instead are known to lie within observable sets. While extant work studied the special cases when the observed sets … Read more

    A Matrix-Free Approach For Solving The Gaussian Process Maximum Likelihood Problem

  • Mihai Anitescu
  • Jie Chen
  • Lei Wang
    • Categories Statistics, Unconstrained Optimization Tags , , , , , ,

    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

    A Matrix-Free Approach For Solving The Gaussian Process Maximum Likelihood Problem

  • Mihai Anitescu
  • Jie Chen
  • Lei Wang
    • Categories Nonlinear Optimization, Statistics, Stochastic Programming Tags , , , , , ,

    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

    A Matrix-Free Approach For Solving The Gaussian Process Maximum Likelihood Problem

  • Mihai Anitescu
    • Categories Nonlinear Optimization, Statistics, Stochastic Programming Tags , , , , , ,

    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

    A Matrix-Free Approach For Solving The Gaussian Process Maximum Likelihood Problem

  • Mihai Anitescu
    • Categories Nonlinear Optimization, Statistics, Stochastic Programming Tags , , , , , ,

    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

    Phylogenetic Analysis Via DC Programming

  • Steven Ellis
  • Madhu Nayakkankuppam
    • Categories Biomedical Applications, Global Optimization Applications Tags , , , ,

    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

    A New Computational Approach to Density Estimation with Semidefinite Programming

  • Tadayoshi Fushiki
  • Takashi Tsuchiya
  • Shingo Horiuchi
    • Categories Data-Mining, Semi-definite Programming, Statistics Tags , , , ,

    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