PhD Defence Rune Christiansen
Causal Inference in the Presence of Hidden Variables: Structure Learning, Effect Estimationand Distribution Generalization
This thesis aims at advancing the field of statistical causality.
Causal modeling is relevant whenever one seeks an understanding not only of how a system evolves by itself, but also how it may respond if some of its components are altered or replaced (‘inter- vened on’). Arguably, such situations are frequently encountered. Inferring causal knowledge from data is a notoriously hard problem, since, even in the limit of infinitely many data, there are typically several compatible causal explanations. Often, this issue is further compounded by incomplete access to all relevant parts of the system (i.e., by the existence of ‘hidden variables’).
This work addresses several open problems related to causal learning in the presence of hidden variables. It consists of three main theoretical contributions. Chapter 2 considers the task of learning causal relations (the ‘causal structure’) from heterogeneous data in cases where these are not known a priori. We exploit a fundamental invariance property which is often assumed of causal regression models. In Chapter 3, we present a causal approach to the problem of distributional robustness, where one aims to learn prediction models that perform well not only on the training data, but also on test data that may come from a different distribution. We use the concept of interventions to model the differences in training and test distribution.
Chapter 4 emerged from discussions with environmental scientists, and is motivated by the question of a causal relationship between armed conflict and tropical forest loss. It resulted in the development of a novel causal framework for spatio-temporal stochastic processes, and a procedure for drawing causal inference from observational spatio-temporal data.
Principal supervisor: Prof. Jonas Peters, University of Copenhagen
Co-supervisor: Prof. Niels Richard Hansen, University of Copenhagen
Prof. Susanne Ditlevsen (chair), University of Copenhagen
Prof. Nicolai Meinshausen, ETH Zurich
Prof. Pierre Pinson, Technical University of Denmark