PhD Defense Jeffrey Glenn Adams
Title: Causal Inference and Causal Discovery with Latent Variables
This thesis contains various results regarding the identifiability of causal models and estimation of causal effects in the presence of latent variables.
First, we study the identifiability of the partially observed linear causal model. In many applications, statistical dependencies between measured variables are partially due to unmeasured confounders or mediators. In order to fully understand the data
generating process, it is desirable to learn not only the causal relations between the observed variables, but also the causal structure of the latent variables. To this end, we present two local graphical conditions that are necessary and sufficient to ensure identifiability of the full graph.
Second, we study the deconfounder algorithm, which was proposed for multiple causal inference in the presence of unmeasured confounding. The deconfounder can be seen as outcome regression adjusted for a substitute confounder which is recovered from the observed treatments. We give theoretical results justifying the use of this method when the treatments are independent when conditioning on the confounter. We also analyze the finite sample error of this estimator in terms of the recovery error of the confounder. The deconfounder is analyzed both from a causal and a causally agnostic perspective.
Third, we study the steady-state distributions of L´evy-driven Ornstein-Uhlenbeck process. We argue that the steady-state interventional distributions of these processes can be expressed in terms of the first two moments of the observational steady-state distribution under a condition we refer to as drift-volatility balance. We derive equations relating higher-order cumulants of the steady-state distributions to the parameters of the stochastic process. From the second- and third-order equations, we derive a rank constraint which holds when drift-volatility balance is satisfied.
Supervisor: Professor Niels Richard Hansen, University of Copenhagen
Assessment Committee:
Associate Professor Niklas Pfister (chair), University of Copenhagen
Professor Mathias Drton, Technical University of Munich
CNRS Researcher Emilie Devijver, Laboratoire d’Informatique de Grenoble