Many datasets are plagued by unobserved confounders: hidden but relevant variables. The presence of hidden variables obscures many conditional independence constraints in the underlying model, and greatly complicates data analysis. In this talk I consider a type of equality constraint which generalizes conditional independence, and which is a ``natural’’ equality constraint for data generated from the marginal distribution of a DAG graphical model.
I discuss applications of such constraints to recovering causal structure from data, and statistical inference in hidden variable models. To this end, I introduce a new kind of graphical model, called the nested Markov model, which is defined via these constraints just as Bayesian networks and Markov random fields are defined via conditional independence constraints.
I describe parameterizations for nested Markov models with discrete state spaces, together with parameter and structure learning algorithms. I show cases where a single generalized equality constraint is sufficient to completely recover a nested Markov model, and thus the corresponding family of hidden variable DAGs.
Part of this material is based on joint work with Thomas S. Richardson, James M. Robins, and Robin J. Evans.
Part of this material is based on joint work with Judea Pearl.
Speaker Biography
Ilya Shpitser is a Lecturer in Statistics at the University of Southampton. His interests include inference in complex multivariate settings, causal inference from observational data, particularly in longitudinal settings, and foundational issues in causality. Previously, Ilya was a research fellow at the causal inference group headed by James M. Robins at the Harvard School of Public Health. He received his PhD under the supervision of Judea Pearl at UCLA.