2016
Journal article  Open Access

Stable graphical models

Misra N., Kuruoglu E. E.

Alpha-stable distribution  Bayesian networks  Non-Gaussian networks  Multivariate analysis  Multivariate distribution  Gene expression modelling 

Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In this paper, we introduce alpha-stable graphical (alpha-SG) models, a class of multivariate stable densities that can also be represented as Bayesian networks whose edges encode linear dependencies between random variables. One major hurdle to the extensive use of stable distributions is the lack of a closed-form analytical expression for their densities. This makes penalized maximumlikelihood based learning computationally demanding. We establish theoretically that the Bayesian information criterion (BIC) can asymptotically be reduced to the computationally more tractable minimum dispersion criterion (MDC) and develop StabLe, a structure learning algorithm based on MDC. We use simulated datasets for ve benchmark network topologies to empirically demonstrate how StabLe improves upon ordinary least squares (OLS) regression. We also apply StabLe to microarray gene expression data for lymphoblastoid cells from 727 individuals belonging to eight global population groups. We establish that StabLe improves test set performance relative to OLS via ten-fold cross-validation. Finally, we develop SGEX, a method for quantifying differential expression of genes between different population groups.

Source: Journal of machine learning research 17 (2016): 1–36.

Publisher: MIT Press,, Cambridge, MA , Stati Uniti d'America



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BibTeX entry
@article{oai:it.cnr:prodotti:359533,
	title = {Stable graphical models},
	author = {Misra N. and Kuruoglu E.  E.},
	publisher = {MIT Press,, Cambridge, MA , Stati Uniti d'America},
	journal = {Journal of machine learning research},
	volume = {17},
	pages = {1–36},
	year = {2016}
}
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