Structure Learning with Bow-free Acyclic Path Diagrams

We consider the problem of structure learning for bow-free acyclic path diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG models that allow for certain hidden variables. We present a first method for this problem using a greedy score-based search algorithm. We also investigate some distributional equivalence properties of BAPs which are used in an algorithmic approach to compute (nearly) equivalent model structures, allowing to infer lower bounds of causal effects. The application of our method to some datasets reveals that BAP models can represent the data much better than DAG models in these cases.

[1]  M. Okamoto.  Distinctness of the Eigenvalues of a Quadratic form in a Multivariate Sample , 1973 .

[2]  Giusi Moffa,et al.  Uniform random generation of large acyclic digraphs , 2012, Statistics and Computing.

[3]  K. Sachs,et al.  Causal Protein-Signaling Networks Derived from Multiparameter Single-Cell Data , 2005, Science.

[4]  Thomas S. Richardson,et al.  Learning high-dimensional directed acyclic graphs with latent and selection variables , 2011, 1104.5617.

[5]  P. Spirtes,et al.  Ancestral graph Markov models , 2002 .

[6]  Richard Scheines,et al.  Causal modeling with the TETRAD program , 1986, Synthese.

[7]  James M. Robins,et al.  Parameter and Structure Learning in Nested Markov Models , 2012, 1207.5058.

[8]  K. Jöreskog.  A general method for analysis of covariance structures , 1970 .

[9]  Robin J. Evans,et al.  Graphs for Margins of Bayesian Networks , 2014, 1408.1809.

[10]  Zoubin Ghahramani,et al.  Bayesian Inference for Gaussian Mixed Graph Models , 2006, UAI.

[11]  Michael Eichler,et al.  Computing Maximum Likelihood Estimates in Recursive Linear Models with Correlated Errors , 2009, J. Mach. Learn. Res..

[12]  Sewall Wright,et al.  Path coefficients and path regressions: Alternative or complementary concepts? , 1960 .

[13]  David Maxwell Chickering,et al.  Learning Bayesian Networks is , 1994 .

[14]  Judea Pearl,et al.  Equivalence and Synthesis of Causal Models , 1990, UAI.

[15]  Mireille Bousquet-Mélou,et al.  Random Generation of Directed Acyclic Graphs , 2001, Electron. Notes Discret. Math..

[16]  P. Spirtes,et al.  Using Path Diagrams as a Structural Equation Modeling Tool , 1998 .

[17]  J. Hanley,et al.  A method of comparing the areas under receiver operating characteristic curves derived from the same cases. , 1983, Radiology.

[18]  O. D. Duncan,et al.  Introduction to Structural Equation Models. , 1977 .

[19]  Peter Bühlmann,et al.  Causal Inference Using Graphical Models with the R Package pcalg , 2012 .

[20]  James M. Robins,et al.  INTRODUCTION TO NESTED MARKOV MODELS , 2014 .

[21]  Tom Claassen,et al.  Learning Sparse Causal Models is not NP-hard , 2013, UAI.

[22]  M. Maathuis,et al.  Estimating high-dimensional intervention effects from observational data , 2008, 0810.4214.