April 20, 2017 @ 11:00 am – 12:00 pm
Rooms 407A/B BAUM
5607 Baum Blvd
Pittsburgh, PA 15206
Toni Porterfield

Center for Causal Discovery
Distinguished Lecture in Causal Discovery
University of Pittsburgh, Carnegie Mellon University,
Pittsburgh Supercomputing Center and Yale University

Thomas Richardson, PhD, Professor and Chair, Department of Statistics, University of Washington, Nested Markov Models at 11:00 am on Thursday, April 20, 2017, in Rooms 407A/B BAUM, 5607 Baum Blvd., The Offices at Baum.

Abstract: Directed acyclic graph (DAG) models may be characterized in several different ways: via a factorization, via d-separation or a local Markov property. It has been known for a long time that marginals of DAG models also imply equality constraints that are not conditional independences. The well-known ‘Verma constraint’ is an example.

In this talk, we will show that equality constraints of this type can be viewed as conditional independences in kernel objects obtained from joint distributions via a fixing operation that generalizes conditioning and marginalization. We use these constraints to define, a graphical model, called the “nested Markov model”, that is associated with acyclic directed mixed graphs (ADMGs).

Naturally associated with a DAG with latent variables, is an ADMG known as the “latent projection”. The nested Markov model associated with an ADMG is a (smooth) supermodel of the model associated with the original latent variable model. Nested Markov models thus constitute a natural class in which to perform causal model search.

This is joint work with Robin Evans (Oxford), James Robins (Harvard) and Ilya Shpitser (Johns Hopkins).

Biography:  Dr.  Richardson is Professor and Chair of the Department of Statistics. He is also an Adjunct Professor in the Departments of Economics and Electrical Engineering and a member of the eScience Steering Committee. He received his BA in Mathematics & Philosophy from the University of Oxford and his MS and PhD in Logic, Computation & Methodology from Carnegie Mellon University. He is a Fellow of the Center for Advanced Studies in the Behavioral Sciences at Stanford University. His research interests include Graphical Models and Causality.


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