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CorrelationCalculator and Filigree: Tools for Data-Driven Network Analysis of Metabolomics Data
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Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs.

Ali Shojaie1, George Michailidis

  • 1Department of Statistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A.

Biometrika
|March 22, 2012
PubMed
Summary

Estimating directed acyclic graphs (DAGs) is challenging. This study introduces an efficient penalized likelihood method for DAG structure estimation in ordered variables, showing adaptive lasso offers superior consistency.

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CorrelationCalculator and Filigree: Tools for Data-Driven Network Analysis of Metabolomics Data
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Published on: November 10, 2023

Area of Science:

  • Computational Statistics
  • Graphical Models
  • Network Inference

Background:

  • Directed acyclic graphs (DAGs) model causal relationships in complex systems.
  • Estimating DAGs from observational data is computationally intensive (NP-hard).
  • Identifiability issues arise as different DAG structures can yield similar observational data.

Purpose of the Study:

  • To develop an efficient penalized likelihood method for estimating DAG adjacency matrices.
  • To address DAG structure estimation when variables possess a natural ordering.
  • To analyze variable selection consistency of penalized methods in high-dimensional sparse settings.

Main Methods:

  • Proposed an efficient penalized likelihood approach for DAG estimation.
  • Investigated the variable selection consistency of lasso and adaptive lasso penalties.
  • Introduced an error-based criterion for tuning parameter selection.

Main Results:

  • The proposed method efficiently estimates DAG adjacency matrices for ordered variables.
  • Lasso penalty shows variable selection consistency only under strict conditions.
  • Adaptive lasso demonstrates consistent estimation of the true graph structure under standard assumptions.

Conclusions:

  • The adaptive lasso penalty provides a robust method for inferring directed acyclic graph structures in ordered, high-dimensional, sparse settings.
  • The proposed penalized likelihood approach offers an efficient solution for a challenging problem in causal inference and network analysis.