Abstract
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 language | English |
|---|---|
| Pages (from-to) | 1291-1314 |
| Number of pages | 24 |
| Journal | Statistica Sinica |
| Volume | 21 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2011 Jul |
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Keywords
- Determinant maximization
- Fourier series
- Graphical model
- Lasso
- Optimal transport
- Structural gradient model
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
A structural model on a hypercube represented by optimal transport. / Sei, Tomonari.
In: Statistica Sinica, Vol. 21, No. 3, 07.2011, p. 1291-1314.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A structural model on a hypercube represented by optimal transport
AU - Sei, Tomonari
PY - 2011/7
Y1 - 2011/7
N2 - 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.
AB - 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.
KW - Determinant maximization
KW - Fourier series
KW - Graphical model
KW - Lasso
KW - Optimal transport
KW - Structural gradient model
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U2 - 10.5705/ss.2009.022
DO - 10.5705/ss.2009.022
M3 - Article
VL - 21
SP - 1291
EP - 1314
JO - Statistica Sinica
JF - Statistica Sinica
SN - 1017-0405
IS - 3
ER -