Causal Structure Learning

Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that represent not only the distribution of the observed system but also the distributions under external interventions. They hence enable predictions under hypothetical interventions, which is important for decision making. The challenging task of learning causal models from data always relies on some underlying assumptions. We discuss several recently proposed structure learning algorithms and their assumptions, and we compare their empirical performance under various scenarios.

[1]  A. Dawid.  Causal Inference without Counterfactuals , 2000 .

[2]  Patrik O. Hoyer,et al.  Estimation of causal effects using linear non-Gaussian causal models with hidden variables , 2008, Int. J. Approx. Reason..

[3]  David Maxwell Chickering,et al.  Learning Equivalence Classes of Bayesian Network Structures , 1996, UAI.

[4]  Tom Burr,et al.  Causation, Prediction, and Search , 2003, Technometrics.

[5]  Kevin P. Murphy,et al.  Exact Bayesian structure learning from uncertain interventions , 2007, AISTATS.

[6]  T. Richardson.  Single World Intervention Graphs ( SWIGs ) : A Unification of the Counterfactual and Graphical Approaches to Causality , 2013 .

[7]  Peter Bühlmann,et al.  Causal stability ranking , 2011, Bioinform..

[8]  J. Robins.  A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect , 1986 .

[9]  Jonas Peters,et al.  BACKSHIFT: Learning causal cyclic graphs from unknown shift interventions , 2015, NIPS.

[10]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[11]  Frederick Eberhardt,et al.  Learning linear cyclic causal models with latent variables , 2012, J. Mach. Learn. Res..

[12]  Jiji Zhang,et al.  On the completeness of orientation rules for causal discovery in the presence of latent confounders and selection bias , 2008, Artif. Intell..

[13]  D. Madigan,et al.  A characterization of Markov equivalence classes for acyclic digraphs , 1997 .

[14]  Marco Scutari,et al.  Learning Bayesian Networks with the bnlearn R Package , 2009, 0908.3817.

[15]  Jonas Peters,et al.  Causal inference by using invariant prediction: identification and confidence intervals , 2015, 1501.01332.

[16]  M. Maathuis,et al.  Estimating the effect of joint interventions from observational data in sparse high-dimensional settings , 2014, 1407.2451.

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

[18]  Naftali Harris,et al.  PC algorithm for nonparanormal graphical models , 2013, J. Mach. Learn. Res..

[19]  Peter Bühlmann,et al.  Characterization and Greedy Learning of Interventional Markov Equivalence Classes of Directed Acyclic Graphs (Abstract) , 2011, UAI.

[20]  Michael I. Jordan.  Graphical Models , 2003 .

[21]  Thomas S. Richardson,et al.  Automated discovery of linear feedback models , 1996 .

[22]  S. Wright.  The Method of Path Coefficients , 1934 .

[23]  Peter Bühlmann,et al.  Predicting causal effects in large-scale systems from observational data , 2010, Nature Methods.

[24]  T. Heskes,et al.  Learning Sparse Causal Models is not NP-hard , 2013, UAI.

[25]  Gregory F. Cooper,et al.  Causal Discovery from a Mixture of Experimental and Observational Data , 1999, UAI.

[26]  D. Rubin.  Causal Inference Using Potential Outcomes , 2005 .

[27]  Jiji Zhang,et al.  Causal Reasoning with Ancestral Graphs , 2008, J. Mach. Learn. Res..

[28]  Peter Bühlmann,et al.  Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm , 2007, J. Mach. Learn. Res..

[29]  Thomas S. Richardson,et al.  Causal Inference in the Presence of Latent Variables and Selection Bias , 1995, UAI.

[30]  Aapo Hyvärinen,et al.  A Linear Non-Gaussian Acyclic Model for Causal Discovery , 2006, J. Mach. Learn. Res..

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

[32]  Alain Hauser,et al.  High-dimensional consistency in score-based and hybrid structure learning , 2015, The Annals of Statistics.

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

[34]  T. Haavelmo,et al.  The probability approach in econometrics , 1944 .

[35]  Jin-Soo Kim,et al.  Analysis of off-target effects of CRISPR/Cas-derived RNA-guided endonucleases and nickases , 2014, Genome research.

[36]  Diego Colombo,et al.  Order-independent constraint-based causal structure learning , 2012, J. Mach. Learn. Res..

[37]  D. A. Kenny,et al.  Correlation and Causation. , 1982 .

[38]  P. Spirtes,et al.  MARKOV EQUIVALENCE FOR ANCESTRAL GRAPHS , 2009, 0908.3605.

[39]  D. A. Kenny,et al.  Correlation and Causation , 1937, Wilmott.

[40]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

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

[42]  Marloes H. Maathuis,et al.  Structure Learning in Graphical Modeling , 2016, 1606.02359.

[43]  Aapo Hyvärinen,et al.  DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model , 2011, J. Mach. Learn. Res..

[44]  Jin Tian,et al.  Causal Discovery from Changes , 2001, UAI.

[45]  David Maxwell Chickering,et al.  Optimal Structure Identification With Greedy Search , 2002, J. Mach. Learn. Res..

[46]  Constantin F. Aliferis,et al.  The max-min hill-climbing Bayesian network structure learning algorithm , 2006, Machine Learning.

[47]  Patrik O. Hoyer,et al.  Discovering Cyclic Causal Models by Independent Components Analysis , 2008, UAI.

[48]  Joshua D. Angrist,et al.  Identification of Causal Effects Using Instrumental Variables , 1993 .