Simultaneous grouping pursuit and feature selection over an undirected graph

Yunzhang Zhu, Xiaotong Shen, Wei Pan

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


In high-dimensional regression, grouping pursuit and feature selection have their own merits while complementing each other in battling the curse of dimensionality. To seek a parsimonious model, we perform simultaneous grouping pursuit and feature selection over an arbitrary undirected graph with each node corresponding to one predictor. When the corresponding nodes are reachable from each other over the graph, regression coefficients can be grouped, whose absolute values are the same or close. This is motivated from gene network analysis, where genes tend to work in groups according to their biological functionalities. Through a nonconvex penalty, we develop a computational strategy and analyze the proposed method. Theoretical analysis indicates that the proposed method reconstructs the oracle estimator, that is, the unbiased least-square estimator given the true grouping, leading to consistent reconstruction of grouping structures and informative features, as well as to optimal parameter estimation. Simulation studies suggest that themethod combines the benefit of grouping pursuit with that of feature selection, and compares favorably against its competitors in selection accuracy and predictive performance. An application to eQTL data is used to illustrate the methodology, where a network is incorporated into analysis through an undirected graph.

Original languageEnglish (US)
Pages (from-to)713-725
Number of pages13
JournalJournal of the American Statistical Association
Issue number502
StatePublished - Dec 16 2013


  • Network analysis
  • Nonconvex minimization
  • Prediction
  • Structured data

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