Likelihood inference for a large causal network

Abstract: Inference of causal relations between interacting units in a directed acyclic graph (DAG), such as a regulatory gene network, is common in practice, imposing challenges because of a lack of inferential tools.In this talk, I will present constrained likelihood ratio tests for inference of the connectivity as well as directionality subject to nonconvex acyclicity constraints in a Gaussian directed graphical model. Particularly,for testing of connectivity, the asymptotic distribution is either chi-squared or normal depending on if the number of testable links in a DAG model is small; for testing of directionality, the asymptotic distribution is the minimum of d independent chi-squared variables with one-degree of freedom or a generalized Gamma distribution depending on if d is small, where d is the number of breakpoints in a hypothesized pathway.Computational methods will be discussed, in addition to some numerical examples to infer a directed pathway in a gene network. This work is joint with Chunlin Li and Wei Pan of the University of Minnesota.

Mathematics

Audience: researchers in the topic

ICCM 2020