PhD Defense Phillip Bredahl Mogensen

Title: Multiple Hypothesis Testing and Causal Discovery

Abstract:

This PhD thesis deals with two different subjects: multiple hypothesis testing and causal discovery.
In the first part of the thesis, we propose a new family of combination tests – called the ‘Too Many, Too Improbable’ (TMTI) test – for combining evidence from multiple hypothesis tests into a single test of a joint hypothesis. We then prove that the proposed family of tests fits within a larger family of tests, for which we prove a quadratic shortcut for carrying out Closed Testing Procedures. Finally, we show empirically that a subfamily of the proposed family can be easily approximated, facilitating
the use of these tests in large-scale studies. In the second part of this thesis, we consider the task of learning
causal graphs from data. First, we attempt to learn finite summary graphs of infinite-dimensional graphs of discrete-time stochastic processes.
We develop simple algorithms that score the existence of causal links by aggregating local linear effects and validate these algorithms on data from a case competition. However, we argue that the observed high performance of these algorithms may be inflated by the presence of an artifact in simulated data. Next, we propose a novel method – called the Invariant Ancestry Search – for learning causal ancestors of a response variable using data sampled from heterogeneous environments. We prove that the proposed method recovers subsets of ancestors of the response with high probability, if given infinite amounts of data, and we show empirically that the guarantees hold approximately when applied to finite
samples.

Thesis 

Academic advisors:  Associate Professor Bo Markussen (primary), University of Copenhagen
Professor Helle Sørensen, University of Copenhagen
Associate Professor Shyam Gopalakrishnan, University of Copenhagen

Assessment committee Professor Niels Richard Hansen (chair), University of Copenhagen
Professor Ingeborg Waernbaum, University of Uppsala
Professor Jelle Goeman, University of Leiden