Due to copyright issues, an electronic copy of the thesis must be ordered from the faculty. For the faculty to have time to process the order, the order must be received by the faculty at the latest 2 days before the public defence. Orders received later than 2 days before the defence will not be processed. After the public defence, please address any inquiries regarding the thesis to the candidate.
Trial Lecture – time and place
See Trial Lecture.
Adjudication committee
- First opponent: Professor Yanyuan Ma, Penn State University, US
- Second opponent: Associate professor Florian Frommlet, Medical University Vienna, Austria
- Third member and chair of the evaluation committee: Professor Tron Anders Moger, University of Oslo
Chair of the Defence
Professor Lene Frost Andersen, University of Oslo
Principal Supervisor
Professor Magne Thoresen, University of Oslo
Summary
In biomedical sciences, advances in high-throughput technology have made it possible to measure large amounts of molecular data, such as gene expression levels or protein abundances, for every cell or organism in a study. This data, often referred to as "omics" data, holds the potential to uncover complex biological mechanisms underlying various diseases. However, a common challenge is that the number of molecular variables far exceeds the number of independent samples, making it difficult for traditional statistical methods to detect reliable patterns in the data. To analyze such high-dimensional data, it is generally assumed that either (1) only a small subset of variables is truly relevant (sparsity principle), or (2) the data can be represented in a lower-dimensional space.
This thesis focuses on variable selection in high-dimensional datasets. The first part is concerned with modeling of longitudinal data, where each participant is observed at multiple time points. Here, it is important to account for the correlation between repeated observations from the same individual to perform effective variable selection. We propose a method based on mixed models to identify important variables while filtering out irrelevant ones. We prove that, under assumption (1), our method can successfully identify the relevant variables with high probability.
The second part of the thesis also addresses correlation, but this time among the high-dimensional variables rather than between observations from the same individual. Here, we assume that both the predictors and the response variable are influenced by a shared set of unobserved latent variables. The number of latent variables is assumed to be much smaller than the number of predictors, thereby satisfying assumption (2). We explore variable selection in this context as well, and show that even without assuming sparsity, methods that produce sparse solutions can still provide good predictions.
Additional information
Contact the research support staff.