A structural model on a hypercube represented by optimal transport

Details A structural model on a hypercube represented by optimal transport A structural model on a hypercube represented by optimal transport

2009-01-29

arxiv.org/abs/0901.4715v1

Statistics

Methodology

28pages, 6figures

Scientific paper

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.

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