Sparse Estimation of Conditional Graphical Models With Application to Gene Networks
In many applications the graph structure in a network arises from two sources: intrinsic connections and connections due to external effects. We introduce a sparse estimation procedure for graphical models that is capable of isolating the intrinsic connections by removing the external effects. Technically, this is formulated as a conditional graphical model, in which the external effects are modeled as predictors, and the graph is determined by the conditional precision matrix. We introduce two sparse estimators of this matrix using the reproduced kernel Hilbert space combined with lasso and adaptive lasso. We establish the sparsity, variable selection consistency, oracle property, and the asymptotic distributions of the proposed estimators. We also develop their convergence rate when the dimension of the conditional precision matrix goes to infinity. The methods are compared with sparse estimators for unconditional graphical models, and with the constrained maximum likelihood estimate that assumes a known graph structure. The methods are applied to a genetic data set to construct a gene network conditioning on single-nucleotide polymorphisms.
If 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.
Volume (Year): 107 (2012)
Issue (Month): 497 (March)
|Contact details of provider:|| Web page: http://www.tandfonline.com/UASA20|
|Order Information:||Web: http://www.tandfonline.com/pricing/journal/UASA20|
When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:107:y:2012:i:497:p:152-167. See general 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: (Michael McNulty)
If references are entirely missing, you can add them using this form.