Parameter and Structure Learning in Nested Markov Models of Acyclic Directed Mixed Graphs

• Activity Number: 463
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Graphics
• Author(s): Ilya Shpitser*+ and Thomas S. Richardson and James Robins and Robin Evans
• Companies: Harvard School of Public Health and University of Washington and HSPH and University of Cambridge
• Keywords: Graphical models ; Causality ; Latent variable models ; Structure learning

Abstract

Models with latent variables can be naturally represented by means of acyclic directed mixed graphs (ADMGs), containing directed arrows representing direct causation, and bidirected arrows representing unobserved confounding. Models represented by ADMGs can contain independence constraints which hold after a generalized conditioning operation called fixing, where a joint distribution is divided by a conditional distribution. Fixing is represented graphically by removing arrows pointing to a fixed node in the graph. Recently, a factorization, and a number of Markov properties were given that capture post-fixing constraints giving a statistical model called the nested Markov model. In this talk, I describe a parameter and structure learning algorithm for discrete nested Markov models. I give a characterization of equivalence classes of graphs of 4 nodes, where all graphs in an equivalence class agree on all independences after sequences of fixings (a generalization of Markov equivalence in DAGs). Finally, I show that even a single post-fixing constraint found in the data can be sufficient to recover the generating causal mechanism of the data by means of a unique ADMG.