Ali Shojaie

An Asymptotically Optimal Coordinate Descent Algorithm for Learning Bayesian Networks from Gaussian Models

  • Tong Xu
  • Simge Küçükyavuz
  • Ali Shojaie
    • Categories (Mixed) Integer Nonlinear Programming

    \(\) This paper studies the problem of learning Bayesian networks from continuous observational data, generated according to a linear Gaussian structural equation model. We consider an \(\ell_0\)-penalized maximum likelihood estimator for this problem which is known to have favorable statistical properties but is computationally challenging to solve, especially for medium-sized Bayesian networks. We propose a … Read more

    Consistent Second-Order Conic Integer Programming for Learning Bayesian Networks

  • Simge Küçükyavuz
  • Ali Shojaie
  • Hasan Manzour
  • Linchuan Wei
  • Hao-Hsiang Wu
    • Categories (Mixed) Integer Nonlinear Programming, Data-Mining, Network Optimization Tags , , , ,

    Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in knowledge discovery. We study the problem of learning the sparse DAG structure of a BN from continuous observational data. The central problem can be modeled as … Read more

    Integer Programming for Learning Directed Acyclic Graphs from Continuous Data

  • Simge Küçükyavuz
  • Hasan Manzour
  • Ali Shojaie
  • Hao-Hsiang Wu
    • Categories (Mixed) Integer Linear Programming, Statistics Tags , , ,

    Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the form of a … Read more