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Title: Estimation of subject-specific directed acyclic graphs with latent effects for discovering causal dependence Authors:  Yuanjia Wang - Columbia University (United States) [presenting]
Abstract: Inferring causal relationship between variables from non-experimental data is a highly challenging goal, especially for large-scale data where estimation of directed acyclic graphs is NP-hard. Under the framework of structural equation models, or functional causal models, we represent joint distribution of variables in causal directed acyclic graphs (DAGs) as a set of structural equations, where directed edges connecting variables depend on subject-specific covariates and unobserved latent variables. The functional causal model framework allows constructing subject-specific DAGs, where the edges representing strength of network connectivity between variables decompose into a fixed effect term (average network effect given covariates), and a random effect term (unobserved residual network effect). Thus, our framework is a mixed effects DAG model. By pooling information across subjects under this model, we can estimate subject-specific network effects with a much better precision and assess heterogeneity of network effects with a better power. We theoretically prove identifiability of our model and propose a penalized likelihood based approach to handle high-dimensionality of the DAG model space, and a fast computational algorithm to achieve hard-thresholding of the edges.