6533b82cfe1ef96bd12900c7
RESEARCH PRODUCT
A computationally fast alternative to cross-validation in penalized Gaussian graphical models
Ernst WitIvan VujacicAntonino Abbruzzosubject
Statistics and ProbabilityFOS: Computer and information sciencesGaussianInformation CriteriaCross-validationMethodology (stat.ME)symbols.namesakeBayesian information criterionStatisticsPenalized estimationGeneralized approximate cross-validationGraphical modelSDG 7 - Affordable and Clean EnergyStatistics - MethodologyMathematics/dk/atira/pure/sustainabledevelopmentgoals/affordable_and_clean_energyKullback-Leibler loApplied MathematicsEstimatorCross-validationGaussian graphical modelSample size determinationModeling and SimulationsymbolsInformation criteriaStatistics Probability and UncertaintyAkaike information criterionSettore SECS-S/01 - StatisticaAlgorithmdescription
We study the problem of selection of regularization parameter in penalized Gaussian graphical models. When the goal is to obtain the model with good predicting power, cross validation is the gold standard. We present a new estimator of Kullback-Leibler loss in Gaussian Graphical model which provides a computationally fast alternative to cross-validation. The estimator is obtained by approximating leave-one-out-cross validation. Our approach is demonstrated on simulated data sets for various types of graphs. The proposed formula exhibits superior performance, especially in the typical small sample size scenario, compared to other available alternatives to cross validation, such as Akaike's information criterion and Generalized approximate cross validation. We also show that the estimator can be used to improve the performance of the BIC when the sample size is small.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-13 |