Istituto di Scienza e Tecnologie dell'Informazione     
Misra N., Kuruoglu E. E. Stable graphical models. In: Journal of Machine Learning Research, vol. 17 (168) pp. 1 - 36. Microtome Publishing, 2016.
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.
URL: http://jmlr.org/papers/v17/14-150.html
Subject Alpha-stable distribution
Bayesian networks
Non-Gaussian networks
Multivariate analysis
Multivariate distribution
Gene expression modelling
G.3 PROBABILITY AND STATISTICS. Multivariate statistics
E.1 DATA STRUCTURES. Graphs and networks
G.2.2 Graph Theory. Network problems
J.3 LIFE AND MEDICAL SCIENCES. Biology and genetics
62F15 Bayesian inference
90B15 Network models, stochastic
60E07 Infinitely divisible distributions; stable distributions
05C80 Random graphs
62P10 Applications to biology and medical sciences
62H10 Multivariate Analysis - Distribution of statistics

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