This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular within the neuroimaging community. Such methods attempt to predict or decode experimentally defined cognitive states based on brain scans. The topics covered in the dissertation are divided into two broad parts:
The first part investigates the relative importance of model selection on the brain patterns extracted form analysis models. Typical neuroimaging data sets are
characterized by relatively few data observations in a high dimensional space. The process of building models in such data sets often requires strong regularization. Often, the degree of model regularization is chosen in order to maximize prediction accuracy. We focus on the relative influence of model regularization parameter choices on the model generalization, the reliability of the spatial brain patterns extracted from the analysis model, and the ability of the resulting model to identify relevant brain networks defining the underlying neural encoding of the experiment. We show that known parts of brain networks can be overlooked in pursuing maximization of prediction accuracy. This supports the view that the quality of spatial patterns extracted from models cannot be assessed purely by focusing on prediction accuracy. Our results instead suggest that model regularization parameters must be carefully selected, so that the model and its visualization enhance our ability to interpret the brain. The second part concerns interpretation of nonlinear models and procedures for
extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map as means for extracting a global summary map from a trained model. Such summary maps provides the investigator with an overview of brain locations of importance to the model’s predictions. The sensitivity map proves as a versatile technique for model visualization. Furthermore, we perform a preliminary investigation of the use of pre-image estimation for lo-
calized interpretation of nonlinear models. In the context of image denoising the pre-image analysis proves to enhance the reliability of brain patterns extracted from multivariate models of the neuroimaging data.