A structural model on a hypercube represented by optimal transport

Tomonari Sei

Research output: Contribution to journalArticlepeer-review


We propose a flexible statistical model for high-dimensional quantitative data on a hypercube. Our model, the structural gradient model (SGM), is based on a one-to-one map on the hypercube that is a solution to an optimal transport problem. As we show with many examples, SGM can describe various dependence structures including correlation and heteroscedasticity. The likelihood function is explicitly expressed without any normalizing constant. Simulation of SGM is achieved through a direct extension of the inverse function method. The maximum likelihood estimation of SGM is reduced to the determinant-maximization known as a convex optimization problem. In particular, a lasso-type estimation is available by adding constraints. SGM is compared with graphical Gaussian models and mixture models.

Original languageEnglish
Pages (from-to)1291-1314
Number of pages24
JournalStatistica Sinica
Issue number3
Publication statusPublished - 2011 Jul
Externally publishedYes


  • Determinant maximization
  • Fourier series
  • Graphical model
  • Lasso
  • Optimal transport
  • Structural gradient model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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