Approximate nonparametric maximum likelihood for mixture models: A convex optimization approach to fitting arbitrary multivariate mixing distributions

Long Feng, Lee H. Dicker

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Nonparametric maximum likelihood (NPML) for mixture models is a technique for estimating mixing distributions that has a long and rich history in statistics going back to the 1950s, and is closely related to empirical Bayes methods. Historically, NPML-based methods have been considered to be relatively impractical because of computational and theoretical obstacles. However, recent work focusing on approximate NPML methods suggests that these methods may have great promise for a variety of modern applications. Building on this recent work, a class of flexible, scalable, and easy to implement approximate NPML methods is studied for problems with multivariate mixing distributions. Concrete guidance on implementing these methods is provided, with theoretical and empirical support; topics covered include identifying the support set of the mixing distribution, and comparing algorithms (across a variety of metrics) for solving the simple convex optimization problem at the core of the approximate NPML problem. Additionally, three diverse real data applications are studied to illustrate the methods’ performance: (i) A baseball data analysis (a classical example for empirical Bayes methods), (ii) high-dimensional microarray classification, and (iii) online prediction of blood-glucose density for diabetes patients. Among other things, the empirical results demonstrate the relative effectiveness of using multivariate (as opposed to univariate) mixing distributions for NPML-based approaches.

Original languageEnglish (US)
Pages (from-to)80-91
Number of pages12
JournalComputational Statistics and Data Analysis
Volume122
DOIs
StatePublished - Jun 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Keywords

  • Convex optimization
  • Kiefer–Wolfowitz estimator
  • Multivariate mixture models
  • Nonparametric maximum likelihood

Fingerprint

Dive into the research topics of 'Approximate nonparametric maximum likelihood for mixture models: A convex optimization approach to fitting arbitrary multivariate mixing distributions'. Together they form a unique fingerprint.

Cite this