1,247
Views
41
CrossRef citations to date
0
Altmetric
Theory and Methods

Learning Sparse Causal Gaussian Networks With Experimental Intervention: Regularization and Coordinate Descent

&
Pages 288-300 | Received 01 Oct 2011, Published online: 15 Mar 2013

REFERENCES

  • Banerjee , O. , El Ghaoui , L. and d’Aspremont , A. 2008 . “Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data,” . Journal of Machine Learning Research , 9 : 485 – 516 .
  • Cooper , G. F. and Herskovits , E. 1992 . “A Bayesian Method for the Induction of Probabilistic Networks From Data,” . Machine Learning , 9 : 309 – 347 .
  • Donoho , D. L. and Johnstone , I. M. 1995 . “Adapting to Unknown Smoothness via Wavelet Shrinkage,” . Journal of the American Statistical Association , 90 : 1200 – 1224 .
  • Efron , B. , Hastie , T. , Johnstone , I. and Tibshirani , R. 2004 . “Least Angle Regression,” . The Annals of Statistics , 32 : 407 – 499 .
  • Ellis , B. 2006 . “Inference on Bayesian Network Structures,” . unpublished Ph.D. dissertation, Harvard University
  • Ellis , B. and Wong , W. H. 2008 . “Learning Causal Bayesian Network Structures From Experimental Data,” . Journal of the American Statistical Association , 103 : 778 – 789 .
  • Fan , J. , Feng , Y. and Wu , Y. 2009 . “Network Exploration via the Adaptive Lasso and SCAD Penalties,” . The Annals of Applied Statistics , 3 : 521 – 541 .
  • Fan , J. and Li , R. 2001 . “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties,” . Journal of the American Statistical Association , 96 : 1348 – 1360 .
  • Friedman , J. , Hastie , T. , Höfling , H. and Tibshirani , R. 2007 . “Pathwise Coordinate Optimization,” . The Annals of Applied Statistics , 1 : 302 – 332 .
  • Friedman , J. , Hastie , T. and Tibshirani , R. 2008 . “Sparse Inverse Covariance Estimation With the Graphical Lasso,” . Biostatistics , 9 : 432 – 441 .
  • Friedman , J. , Hastie , T. and Tibshirani , R. 2010 . “Regularization Paths for Generalized Linear Models via Coordinate Descent,” . Journal of Statistical Software , 33 : 1 – 22 .
  • Friedman , N. and Koller , D. 2003 . “Being Bayesian About Network Structure: A Bayesian Approach to Structure Discovery in Bayesian Networks,” . Machine Learning , 50 : 95 – 125 .
  • Fu , W. 1998 . “Penalized Regressions: The Bridge versus the Lasso,” . Journal of Computational and Graphical Statistics , 7 : 397 – 416 .
  • Hauser , A. and Bühlmann , P. 2012 . “Characterization and Greedy Learning of Interventional Markov Equivalence Classes of Directed Acyclic Graphs,” . Journal of Machine Learning Research , 13 : 2409 – 2464 .
  • Heckerman , D. , Geiger , D. and Chickering , D. M. 1995 . “Learning Bayesian Networks: The Combination of Knowledge and Statistical Data,” . Machine Learning , 20 : 197 – 243 .
  • Kalisch , M. and Bühlmann , P. 2007 . “Estimating High-Dimensional Directed Acyclic Graphs With the PC-Algorithm,” . Journal of Machine Learning Research , 8 : 613 – 636 .
  • Kalisch , M. , Mächler , M. , Colombo , D. , Maathuis , M. H. and Bühlmann , P. 2012 . “Causal Inference Using Graphical Models With the R Package pcalg,” . Journal of Statistical Software , 47 : 1 – 26 .
  • Lam , C. and Fan , J. 2009 . “Sparsistency and Rates of Convergence in Large Covariance Matrix Estimation,” . The Annals of Statistics , 37 : 4254 – 4278 .
  • Lam , W. and Bacchus , F. 1994 . “Learning Bayesian Belief Networks: An Approach Based on the MDL Principle,” . Computational Intelligence , 10 : 269 – 293 .
  • Lauritzen , S. L. 1996 . Graphical Models , Oxford : Oxford University Press .
  • Madigan , D. and York , J. 1995 . “Bayesian Graphical Models for Discrete Data,” . International Statistical Review , 63 : 215 – 232 .
  • Meinshausen , N. and Bühlmann , P. 2006 . “High-Dimensional Graphs and Variable Selection With the Lasso,” . The Annals of Statistics , 34 : 1436 – 1462 .
  • Pearl , J. 2000 . Causality: Models, Reasoning, and Inference , New York : Cambridge University Press .
  • Robinson , R. W. 1973 . “Counting Labeled Acyclic Digraphs,” . In New Directions in the Theory of Graphs , Edited by: Haray , F. 239 – 273 . New York : Academic Press .
  • Sachs , K. , Perez , O. , Pe’er , D. , Lauffenburger , D. A. and Nolan , G. P. 2005 . “Causal Protein-Signaling Networks Derived From Multiparameter Single-Cell Data,” . Science , 308 : 523 – 529 .
  • Shojaie , A. and Michailidis , G. 2010 . “Penalized Likelihood Methods for Estimation of Sparse High-Dimensional Directed Acyclic Graphs,” . Biometrika , 97 : 519 – 538 .
  • Spirtes , P. , Glymour , C. and Scheines , R. 1993 . Causation, Prediction, and Search , New York : Springer .
  • Tibshirani , R. 1996 . “Regression Shrinkage and Selection via the Lasso,” . Journal of the Royal Statistical Society, Series B , 58 : 267 – 288 .
  • Tseng , P. 2001 . “Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization,” . Journal of Optimization Theory and Applications , 109 : 475 – 494 .
  • Vandenberghe , L. , Boyd , S. and Wu , S.-P. 1998 . “Determinant Maximization With Linear Matrix Inequality Constraints,” . SIAM Journal on Matrix Analysis and Applications , 19 : 499 – 533 .
  • Wu , T. and Lange , K. 2008 . “Coordinate Descent Procedures for Lasso Penalized Regression,” . The Annals of Applied Statistics , 2 : 224 – 244 .
  • Yuan , M. and Lin , Y. 2007 . “Model Selection and Estimation in the Gaussian Graphical Model,” . Biometrika , 94 : 19 – 35 .
  • Zhou , Q. 2011 . “Multi-Domain Sampling With Applications to Structural Inference of Bayesian Networks,” . Journal of the American Statistical Association , 106 : 1317 – 1330 .
  • Zou , H. 2006 . “The Adaptive Lasso and Its Oracle Properties,” . Journal of the American Statistical Association , 101 : 1418 – 1429 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.