Network exploration via the adaptive LASSO and SCAD penalties

Jianqing Fan, Yang Feng, Yichao Wu

Research output: Contribution to journalArticlepeer-review

236 Scopus citations


Graphical models are frequently used to explore networks, such as genetic networks, among a set of variables. This is usually carried out via exploring the sparsity of the precision matrix of the variables under consideration. Penalized likelihood methods are often used in such explorations. Yet, positive-definiteness constraints of precision matrices make the optimization problem challenging. We introduce nonconcave penalties and the adaptive LASSO penalty to attenuate the bias problem in the network estimation. Through the local linear approximation to the nonconcave penalty functions, the problem of precision matrix estimation is recast as a sequence of penalized likelihood problems with a weighted L 1 penalty and solved using the efficient algorithm of Friedman et al. [Biostatistics 9 (2008) 432-441]. Our estimation schemes are applied to two real datasets. Simulation experiments and asymptotic theory are used to justify our proposed methods.

Original languageEnglish (US)
Pages (from-to)521-541
Number of pages21
JournalAnnals of Applied Statistics
Issue number2
StatePublished - Mar 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty


  • Adaptive LASSO
  • Covariance selection
  • Gaussian concentration graphical model
  • Genetic network
  • Precision matrix
  • SCAD


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