The Bayesian group-Lasso for analyzing contingency tables

ABSTRACT

Group-Lasso estimators, useful in many applications, suffer from lack of meaningful variance estimates for regression coefficients. To overcome such problems, we propose a full Bayesian treatment of the Group-Lasso, extending the standard Bayesian Lasso, using hierarchical expansion. The method is then applied to Poisson models for contingency tables using a highly efficient MCMC algorithm. The simulated experiments validate the performance of this method on artificial datasets with known ground-truth. When applied to a breast cancer dataset, the method demonstrates the capability of identifying the differences in interactions patterns of marker proteins between different patient groups.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.6 Learning

Additional Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Probabilistic algorithms (including Monte Carlo); Markov processes

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.4 Model Validation and Analysis
      I.6.5 Model Development
          Subjects: Modeling methodologies
      I.6.6 Simulation Output Analysis

General Terms:
Algorithms, Design, Performance, Theory