CDS&E-MSS: Causal learning and inference on complex observational data

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Learning the causal relations among a set of variables from given data is a fundamental problem in scientific research and engineering. Directed acyclic graphs (DAGs) are a popular class of mathematical models for causal networks, in which a directed link encodes a cause-effect relation between two variables. Although experimental intervention provides a direct means to causal inference, such experiments are often not available or limited in many domains. Consequently, structure learning of causal networks from observational data is an important and active research area in statistics and data science. This project targets a few notorious difficulties in causal network learning from observational data, namely the high-dimensionality, nonlinearity and potential dependence in the data. Novel statistical methods and theory for causal structure learning and causal inference will be developed to overcome these difficulties. Software packages will be released to provide efficient implementation of the methods and algorithms. To handle high-dimensionality, instead of estimating the structure of a full DAG, the PI will develop a set of methods for local structure learning that identifies the causal parents of target variables, followed by causal effect estimation given the estimated parent sets. Leveraging recent identifiability results for nonlinear and non-Gaussian DAGs, a sequential Monte Carlo method will be developed to sample causal orders and to estimate the joint intervention effects of a set of variables given a partial causal ordering. To accommodate data dependence among individuals, the DAG model will be generalized to network data via the Kronecker product of graphical models. An algorithm will be developed to estimate parameters and DAG structure under this new model, which iterates between a de-correlation step to remove data dependence and a DAG learning step by a standard method. Theoretical results will be established for the local structure and causal order estimation methods and to justify the de-correlation approach. The project integrates structure learning of graphical models, Monte Carlo methods, nonconvex optimization, nonparametric regression, and conditional independence test into causal discovery and inference on observational data. Moreover, many components in this project are well-motivated by recent single-cell RNA-sequencing data and the construction of causal networks for gene regulation. Application of the methods to the fast accumulating single-cell RNA-sequencing data will produce reliable and accurate inference for the causality of gene expression, which is a fundamental problem in molecular biology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.