1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Cognitive Systems, Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Copenhagen Center for Health Technology, Center, Technical University of Denmark
This Ph.D. thesis, A Multivariate Approach to Functional Neuro Modeling, deals with the analysis and modeling of data from functional neuro imaging experiments. A multivariate dataset description is provided which facilitates efficient representation of typical datasets and, more importantly, provides the basis for a generalization theoretical framework relating model performance to model complexity and dataset size. Briefly summarized the major topics discussed in the thesis include: - An introduction of the representation of functional datasets by pairs of neuronal activity patterns and overall conditions governing the functional experiment, via associated micro- and macroscopic variables. The description facilitates an efficient microscopic re-representation, as well as a handle on the link between brain and behavior; the latter is achieved by hypothesizing variations in the micro- and macroscopic variables to be manifestations of an underlying system. - A review of two microscopic basis selection procedures, namely principal component analysis and independent component analysis, with respect to their applicability to functional datasets. - Quantitative model performance assessment via a generalization theoretical framework centered around measures of model generalization error. - Only few, if any, examples of the application of generalization theory to functional neuro modeling currently exist in the literature. - Exemplification of the proposed generalization theoretical framework by the application of linear and more flexible, nonlinear microscopic regression models to a real-world dataset. The dependency of model performance, as quantified by generalization error, on model flexibility and training set size is demonstrated, leading to the important realization that no uniformly optimal model exists. - Model visualization and interpretation techniques. The simplicity of this task for linear models contrasts the difficulties involved when dealing with nonlinear models. Finally, a visualization technique for nonlinear models is proposed. A single observation emerges from the thesis as particularly important; optimal model flexibility is a function of both the complexity and the size of the dataset at hand. This is something that has not received appropriate attention by the functional neuro modeling community so far. The observation implies that optimal model performance rarely is achieved with black-box models; rather, model flexibility must be matched to the specific functional dataset. The potential advantage is a model that more precisely approximates the true nature of the relationship between brain and behavior, thus paving the way for increased insight into the function of the human brain.