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

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  • 1Carnegie Mellon University, Pittsburgh, PA 15213.

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|August 26, 2014
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Summary
This summary is machine-generated.

Choosing the right regularization parameter for high-dimensional graphical models is tough. StARS, a new stability-based method, reliably selects this parameter, outperforming traditional techniques like K-fold cross-validation.

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Area of Science:

  • Statistical inference
  • Machine learning
  • Network analysis

Background:

  • Estimating high-dimensional graphical models requires careful selection of regularization parameters.
  • Traditional methods like K-fold cross-validation (K-CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC) are often inadequate in high-dimensional settings.

Purpose of the Study:

  • To introduce StARS, a novel stability-based method for data-dependent regularization parameter selection in high-dimensional undirected graphical models.
  • To provide a method with a clear interpretation: selecting the minimal regularization for a sparse and replicable graph.

Main Methods:

  • The StARS method assesses graph stability across subsamples to determine the optimal regularization parameter.
  • Theoretical analysis demonstrates partial sparsistency under mild conditions, ensuring true edges are captured.

Main Results:

  • StARS demonstrates superior performance compared to K-CV, AIC, and BIC on synthetic and real microarray data.
  • The method ensures graph sparsity and replicability with minimal regularization.

Conclusions:

  • StARS offers a robust and effective solution for regularization parameter selection in high-dimensional graphical models.
  • The proposed method outperforms existing state-of-the-art procedures, particularly in high-dimensional scenarios.