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Estimation of High-Dimensional Graphical Models Using Regularized Score Matching.

Lina Lin1, Mathias Drton1, Ali Shojaie2

  • 1Department of Statistics, University of Washington, Seattle, WA 98195, U.S.A.

Electronic Journal of Statistics
|June 23, 2017
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Summary
This summary is machine-generated.

We introduce regularized score matching, a new method for estimating graphical models. This technique efficiently handles continuous data and non-Gaussian models, offering state-of-the-art performance in various settings.

Keywords:
Conditional independence graphexponential familygraphical modelhigh-dimensional statisticsscore matchingsparsity

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Area of Science:

  • Statistics
  • Machine Learning
  • Computational Biology

Background:

  • Graphical models represent complex variable dependencies.
  • Existing methods for estimating undirected graphs can face asymmetry or computational challenges.

Purpose of the Study:

  • Introduce regularized score matching for estimating undirected conditional independence graphs.
  • Provide a computationally efficient method for continuous observations, including non-Gaussian models.

Main Methods:

  • Utilize score matching loss for graph estimation.
  • Apply L1 regularization for sparse, high-dimensional settings.
  • Develop a method applicable to continuous observations and non-Gaussian exponential family models.

Main Results:

  • Regularized score matching avoids asymmetry issues present in neighborhood selection.
  • The method offers a quadratic loss with piecewise linear solution paths under L1 regularization.
  • Demonstrated consistency for graph estimation in sparse high-dimensional settings under irrepresentability conditions.

Conclusions:

  • Regularized score matching achieves state-of-the-art performance in Gaussian graphical models.
  • The method is a valuable tool for efficient estimation in non-Gaussian graphical models.
  • Validated through numerical experiments and RNAseq data analysis.