Modeling Discrete Interventional Data using Directed Cyclic Graphical Models

We outline a representation for discrete multivariate distributions in terms of interventional potential functions that are globally normalized. This representation can be used to model the effects of interventions, and the independence properties encoded in this model can be represented as a directed graph that allows cycles. In addition to discussing inference and sampling with this representation, we give an exponential family parametrization that allows parameter estimation to be stated as a convex optimization problem; we also give a convex relaxation of the task of simultaneous parameter and structure learning using group l1-regularization. The model is evaluated on simulated data and intracellular flow cytometry data.

[1]  Robert H. Strotz,et al.  Recursive versus non-recursive systems: An attempt at a synthesis , 2017 .

[2]  J. Besag.  Statistical Analysis of Non-Lattice Data , 1975 .

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

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

[5]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  G. B. Smith,et al.  Preface to S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images” , 1987 .

[7]  Peter Spirtes,et al.  Directed Cyclic Graphical Representations of Feedback Models , 1995, UAI.

[8]  Thomas S. Richardson,et al.  A Discovery Algorithm for Directed Cyclic Graphs , 1996, UAI.

[9]  Thomas Richardson.  A Polynomial-Time Algorithm for Deciding Equivalence of Directed Cyclic Graphical Models , 1996, UAI.

[10]  Rina Dechter,et al.  Identifying Independencies in Causal Graphs with Feedback , 1996, UAI.

[11]  Thomas S. Richardson,et al.  A Polynomial-Time Algorithm for Deciding Markov Equivalence of Directed Cyclic Graphical Models , 1996, UAI 1996.

[12]  Volker Tresp,et al.  Nonlinear Markov Networks for Continuous Variables , 1997, NIPS.

[13]  Michael I. Jordan.  Graphical Models , 1998 .

[14]  David Maxwell Chickering,et al.  Dependency Networks for Inference, Collaborative Filtering, and Data Visualization , 2000, J. Mach. Learn. Res..

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

[16]  B. Arnold,et al.  Conditionally specified distributions: an introduction , 2001 .

[17]  S. Lauritzen,et al.  Chain graph models and their causal interpretations , 2002 .

[18]  Brendan J. Frey,et al.  Extending Factor Graphs so as to Unify Directed and Undirected Graphical Models , 2002, UAI.

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

[20]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[21]  M. Yuan,et al.  Model selection and estimation in regression with grouped variables , 2006 .

[22]  Daphne Koller,et al.  Efficient Structure Learning of Markov Networks using L1-Regularization , 2006, NIPS.

[23]  Tomi Silander,et al.  A Simple Approach for Finding the Globally Optimal Bayesian Network Structure , 2006, UAI.

[24]  Thomas Hofmann,et al.  Efficient Structure Learning of Markov Networks using L1-Regularization , 2007 .

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

[26]  Mark W. Schmidt,et al.  Structure learning in random fields for heart motion abnormality detection , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

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

[28]  Mark W. Schmidt,et al.  Optimizing Costly Functions with Simple Constraints: A Limited-Memory Projected Quasi-Newton Algorithm , 2009, AISTATS.

[29]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .