Causal glms within a graphical modelling framework

Abstract

Invariance of causal models under heterogeneous settings has been exploited by a number of recent methods for causal discovery. Most of these methods assume linear dependences between the variables in the system and focus on recovering the causal parents of a target variable. In this talk, I present an extension of a causal graphical model framework to the case where the target variable is described by a generalized linear model conditional on its causal parents, while no other linear assumptions are made. Under this setting, we characterize the causal model uniquely by means of two key properties, invariance of the Pearson residuals statistics and maximum of the population likelihood. These two properties form the basis of a computationally efficient strategy for searching the causal model among all possible models. Crucially, for generalized linear models with a known dispersion parameter, such as Poisson or logistic regression, the causal model can be identified from a single environment. This overcomes the challenge of requiring observational data from a number of sufficiently different environments.