Representation of context-specific graphical causal models with observational and interventional data

Graphical models are multivariate statistical models where conditional independence relations among random variables are represented by the missing edges of a graph whose nodes are the random variables. When the graph used to represent the model is a directed acyclic graph (DAG) these models are also useful to represent causal relations. This causal interpretation makes these models useful in areas such as genomics, psychology, and epidemiology. When the random variables under consideration are all discrete, it is useful, for modelling purposes, to consider a more general form of conditional independence called context-specific independence. Encoding context-specific independence using graphical models is an interesting challenge which has been considered previously by Heckerman (1990), Geiger and Heckerman (1996), Boutelier et al (1996), Smith and Anderson (2008), and Pensar et al 2015. The goal of this talk is to present a new way of representing context-specific causal models. We prove that these models generalize several important properties of graphical models and present a way to model interventions in these models. This is joint work with Liam Solus (KTH, Sweden).