Determinantal point processes and their parameter estimations

• Author / Creator

  Shi, Haiyi

• Determinantal point processes (DPPs) arise as important tools in various aspects of mathematics, such as stochastic processes, random matrices, and combinatorics. Over the last decade, DPPs have also been widely used in ma- chine learning community; they are especially popular in subset selection prob- lems, for they favour subsets of high quality and diversity. These applications motivate studies in parameter estimations, of which a common method is max- imum likelihood estimation. In 2017, Brunel et al first studied this non-convex optimization problem using an information geometric approach. Inspired by their work, we introduce and extend some of their results: we exhibit the strong consistency and the rates of convergence of the maximum likelihood es- timator to the normality, i.e. the Berry-Essen type theorem. Moreover, in two dimensional case, we obtain the explicit form of the estimator and establish the strong consistency and central limit theorem. We also give some remarks on higher dimensional DPPs.

• Subjects / Keywords

  • Determinantal point processes
  • Parameter estimations

• Graduation date

  Fall 2023

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-md2b-gs94

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.