The cost of using decomposable Gaussian graphical models for computational convenience
AbstractGraphical models are a powerful tool for describing patterns of conditional independence, and can also be used to regularize the covariance matrix. Vertices in the graph represent variables, and in the Gaussian setting, edges between vertices are equivalent to non-zero elements in the inverse covariance matrix. Models that can be represented as a decomposable (triangulated) graph are more computationally tractable; in fact, in the high-dimensional Bayesian setting it is common to restrict model selection procedures to decomposable models. We consider estimation of the covariance and inverse covariance matrix where the true model forms a cycle, but estimation is performed supposing that the pattern of zeros is a decomposable graphical model, where the elements restricted to zero are a subset of those in the true matrix. The variance of the maximum likelihood estimator based on the decomposable model is demonstrably larger than for the true non-decomposable model, and which decomposable model is selected affects the variance of particular elements of the matrix. When estimating the inverse covariance matrix the cost in terms of accuracy for using the decomposable model is fairly small, even when the difference in sparsity is large and the sample size is fairly small (e.g., the true model is a cycle of size 50, and the sample size is 51). However, when estimating the covariance matrix, the estimators for most elements had a dramatic increase in variance (200-fold in some cases) when a decomposable model was substituted. These increases become more pronounced as the difference in sparsity between models increases.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 56 (2012)
Issue (Month): 8 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/csda
Graphical model; Covariance selection; Decomposable models; Regularization; Small-sample inference;
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.