Probabilistic Methods for Image and Signal ClassificationApplications to Medicine and Volcanology

Abstract

Probabilistic methods have achieved empirical success in many predictive modeling and inference tasks. Prominent among probabilistic classifiers are Gaussian Processes (GPs). They are popular because of their expressiveness and the possibility of introducing prior beliefs. They use (probabilistic) uncertainty in modeling and inference. However, GPs can not easily estimate complex functions with stationary kernels. To overcome this limitation, Deep Gaussian Processes (DGPs) arise as their hierarchical extension. They combine the complexity of deep models while retaining the advantages of GPs. Many areas of study take advantage of these models to solve decision-making problems. This thesis proposes and studies probabilistic methods based on GPs and DGPs for classification problems which range from supervised to weakly supervised ones. The studied models cover realistic annotation scenarios: an expert provides labels for all samples, an expert provides only label for bags of samples, and finally, multiple expert and nonexpert participants provide annotations, which may not agree. The data utilized in this thesis come from: volcanology, where we have access to fully annotated data sets, histology, where to alleviate the annotation task, several medical students are asked to annotate the images and computerized tomography, where annotations are provided at scan but not slide level. We find that probabilistic models based on GPs and DGPs outperform state-of-the-art Deep Learning models for these problems.