Identification and Statistical Inference in Graphical Models with Feedback and Latent Variables

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The last decade has seen great advances in scientific experimentation. In biology, for instance, it has become routine to collect complex data that simultaneously quantify the levels of expression of many genes or proteins. This project addresses the development of statistical methodology that allows processing of such data to obtain insights on cause-effect relationships among the units in the studied system. Specifically, the proposed research addresses two key challenges, namely, how to tackle problems in which some important variables remain unobserved, and how to cope with the presence of causal feedback loops. The research develops statistical techniques to infer cause-effect relationships and expands our understanding of which conclusions may possibly be reached under imperfect information.Both feedback and latent variables bring about great challenges in graphical modeling because, in their presence, consideration of conditional independence is no longer sufficient to characterize and compare models. This project focuses on linear models that allow for refined modeling of feedback loops and/or the effects of latent variables. The PI will develop criteria for parameter identifiability, which is no longer guaranteed with feedback or latent variables. The work will also determine conditions for when a model is of expected dimension as given by a parameter count. Knowledge of dimension is needed for instance when setting degrees of freedom in statistical tests. Next, the project will lead to a better understanding of constraints other than conditional independence. Finally, the PI will develop new model selection methods in Gaussian as well non-Gaussian models.