Title: Bayesian graphical modelling for heterogeneous causal effects
Authors: Guido Consonni - Universita Cattolica del Sacro Cuore (Italy)
Federico Castelletti - Università Cattolica del Sacro Cuore (Milan) (Italy) [presenting]
Abstract: A Directed Acyclic Graph (DAG) provides an effective framework for analyzing causal relations among variables based on observational data. In particular, the effect on a response due to a hypothetical intervention on a variable in the system can be meaningfully addressed. We account for uncertainty on the DAG structure, and we overcome the usual assumption that the graph is common to all observations by allowing for heterogeneity of the underlying population. We consider a Dirichlet Process (DP) mixture of DAG models, where each component of the mixture is a Gaussian DAG model, with cluster-specific conditional independencies encoded by the DAG. Our methodology allows us to identify homogeneous sub-groups of individuals, each having a distinct causal effect following an intervention on a target variable. The inference is based on Normal-DAG-Wishart priors for the mean and the Cholesky parameters of each Gaussian DAG model. Lack of identifiability of the underlying DAG due to observational data and computational issues are discussed. An application to protein expression data from Acute Myeloid Leukemia (AML) patients is presented, with the aim of producing estimates of cluster-specific causal effects on disease progression following interventions on targeted proteins.