Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models

Details Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models

2010-06-16

arxiv.org/abs/1006.3316v1

Statistics

Machine Learning

Scientific paper

A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include $K$-fold cross-validation ($K$-CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Though these methods work well for low-dimensional problems, they are not suitable in high dimensional settings. In this paper, we present StARS: a new stability-based method for choosing the regularization parameter in high dimensional inference for undirected graphs. The method has a clear interpretation: we use the least amount of regularization that simultaneously makes a graph sparse and replicable under random sampling. This interpretation requires essentially no conditions. Under mild conditions, we show that StARS is partially sparsistent in terms of graph estimation: i.e. with high probability, all the true edges will be included in the selected model even when the graph size diverges with the sample size. Empirically, the performance of StARS is compared with the state-of-the-art model selection procedures, including $K$-CV, AIC, and BIC, on both synthetic data and a real microarray dataset. StARS outperforms all these competing procedures.

Affiliated with

Also associated with

No associations

Rating

Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-550824