Statistical Learning with Applications in Biology
In DTU Compute PHD-2018, 2019
Abstract
Statistical methods are often motivated by real problems. We consider methods inspired by problems in biology and medicine. The thesis is in two parts. In the first part we consider data in the form of graphs (or networks). These occur naturally in many contexts such as social and biological networks. We specifically consider the setting where we have multiple graphs on the same set of nodes. We propose a model in this setting called the multiple random dot product graph model. Fitting the model is an optimization problem which we solve efficiently using a new alternating minimization algorithm. A hypothesis test in the model framework for whether two graphs are drawn from the same distribution is also proposed. Both the fitting algorithm and test are evaluated in simulation studies. The model is also generalized to weighted graphs where we specifically consider Poisson and normally distributed weights. Similar hypothesis tests are proposed in these settings and again we evaluate the performance through simulation studies. The second part of the thesis considers prediction of disease progression. We compare three common approaches for disease prediction and apply them to a diabetes data set. In this data, the time until a patient goes on to insulin treatment is of interest - especially whether progression is fast or slow. The methods are: A Cox proportional hazards model, a random forest method for survival data, and a neural network approach. The prediction performance, and the pros and cons of the methods are discussed.
Info
Thesis PhD, 2019
In DTU Compute PHD-2018, 2019
UN SDG Classification
DK Main Research Area
Science/Technology
