AUTHORS: Niels Mørch
Department of Mathematical Modelling, Building 321
Technical University of Denmark, DK-2800 Lyngby, Denmark
emails: nmorch@imm.dtu.dk
www: http://eivind.imm.dtu.dk
ABSTRACT:
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.