A structural model on a hypercube represented by optimal transport
Methodology
2009-01-30 v1 Statistics Theory
Statistics Theory
Abstract
We propose a flexible statistical model for high-dimensional quantitative data on a hypercube. Our model, called the structural gradient model (SGM), is based on a one-to-one map on the hypercube that is a solution for an optimal transport problem. As we show with many examples, SGM can describe various dependence structures including correlation and heteroscedasticity. The maximum likelihood estimation of SGM is effectively solved by the determinant-maximization programming. In particular, a lasso-type estimation is available by adding constraints. SGM is compared with graphical Gaussian models and mixture models.
Keywords
Cite
@article{arxiv.0901.4715,
title = {A structural model on a hypercube represented by optimal transport},
author = {Tomonari Sei},
journal= {arXiv preprint arXiv:0901.4715},
year = {2009}
}
Comments
28pages, 6figures