CMX Student/Postdoc Seminar
Latent-variable modeling: causality, robustness, and false discovery methods
Many driving factors of physical systems are often latent or unobserved. Thus, understanding such systems and producing robust predictions crucially relies on accounting for the influence of the latent structure. I will discuss methodological and theoretical advances in two central problems in latent-variable modeling. The first problem aims to estimate causal relations among a collection of observed variables with latent effects. Given access to heterogeneous data arising from perturbations, I introduce a maximum-likelihood framework that provably identifies the underlying causal structure. Unlike previous techniques, this procedure allows for perturbations on all of the variables. The second problem focuses on developing false discovery methods for latent-variable models that are parameterized by low-rank matrices, where the traditional perspective on false discovery control is ill-suited due to the non-discrete nature of the underlying decision spaces. To overcome this challenge, I present a geometric reformulation of the notion of a discovery as well as a specific algorithm to control false discoveries in these settings. Throughout, I will explore the utility of the proposed methodologies for real-world applications such as California reservoir modeling.