PhD Defense: Nikolaj Theodor Birkmose Thams
Title: Causality and Distribution Shift
This PhD thesis contains a number of contributions on drawing causal inference from observational data, with a particular focus on shifts in distribution. These contributions fall within three categories: 1) Testing hypotheses in shifted distributions, 2) learning predictive models that are robust to distribution shift and 3) inferring causal structure and causal effects using exogenous variables. First, we present a general framework which formalizes statistical hypothesis testing under distribution shifts. We propose methods and prove theoretical results for conducting such tests. We describe a number of different applications of testing under distribution shifts, which includes policy learning and conditional independence testing.
Second, we outline ways of using causal methodology to learn predictive models that are robust to shifts in distribution. We propose an algorithm for learning invariant policies in bandit problems, and we show that, if certain assumptions are satisfied, this allows for worst-case optimal prediction in unseen environments. In a regression setting, we propose an estimator for learning linear predictors that are worst-case optimal over a class of mean-shifts in an unobserved confounder, assuming that we observe proxies of this confounder. We also propose a framework for specifying plausible parametric shifts in distribution and develop theory for finding the shift that has the worst-case impact on the performance of a predictive model.
Finally, we provide methods for inferring causal structure and causal effects from heterogeneous observational data. We propose a procedure for identifying causal ancestors of a given target variable by using ‘minimal invariance’ of sets of predictors across multiple exogenous environments (or distribution shifts). We develop instrumental variable methodology for inferring causal effects in linear time series data, where we highlight that past states are helpful for obtaining ‘more exogeneity’ but also that past states confound the instrument and outcome and needs to be adjusted for.
The defence will be held as a hybrid defence.
Supervisor: Professor Jonas Peters, University of Copenhagen
Assessment Committee:
Professor Susanne Ditlevsen (chair), University of Copenhagen
Professor Thomas Richardson, University of Washington
Professor Rajen Shah, University of Cambridge