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Title: Direct estimation of differences in causal graphs Authors:  Yuhao Wang - MIT (United States) [presenting]
Chandler Squires - MIT (United States)
Anastasiya Belyaeva - MIT (United States)
Caroline Uhler - Massachusetts Institute of Technology (United States)
Abstract: The problem of estimating the differences between two causal directed acyclic graph (DAG) models given i.i.d. samples from each model is considered. This is of interest for example in genomics, where changes in the structure or edge weights of the underlying causal graphs reflect alterations in the gene regulatory networks. We provide the first provably consistent method for directly estimating the differences in a pair of causal DAGs without separately learning two possibly large and dense DAG models and computing their difference. Our two-step algorithm first uses invariance tests between regression coefficients of the two data sets to estimate the skeleton of the difference graph and then orients some of the edges using invariance tests between regression residual variances. We demonstrate the properties of our method through a simulation study and apply it to the analysis of gene expression data from ovarian cancer and during T-cell activation.