Over the last two decades, Functional Magnetic Resonance Imaging (fMRI) has revolutionized the study of the brain. This non-invasive technique produces snapshots of brain activity over time, allowing researchers to literally peer into the mind as it performs everyday tasks like reading or viewing images. Gradually the need has emerged for fMRI analysis techniques that model activity occurring at numerous locations throughout the brain simultaneously, and make predictions about what a person is doing or thinking solely from his or her brain activity, or "mind read." Machine learning techniques can accomplish both these goals, and thus have become a popular modeling choice; however, most standard machine learning algorithms were designed for problems in which there are relatively few candidate predictor variables, and the modeling objective is to make accurate predictions.
In fMRI data, the number of predictor variables can be very large, while the likely number of relevant predictors may be quite small. Furthermore, machine learning algorithms are increasingly being employed in the natural sciences, and while accurate predictions can serve to validate scientific models, the end goal of such modeling is usually to interpret the models to gain scientific insight. An emerging class of algorithms were designed to address the challenge of learning from and interpreting models with large predictor sets by building sparse models in which only a small subset of predictors are used. However, interpretation of such models still poses challenges; in particular, such models are often not reliable across datasets, limiting their usefulness as scientific models of brain functioning.
An additional challenge for fMRI modeling is that fMRI data are known to exhibit strong spatial structure, especially in the form of spreading of activity across localized areas of the brain. This phenomenon is generally understood, but the properties remain poorly specified and are known to vary by factors such as the person studied (subject), mental task, and brain region considered. Ultimately, better characterization of this spatial structure is warranted because it presents both a modeling confound and an inherently intriguing aspect of neural functioning.
In this thesis, we explore the interaction between prediction, sparsity, spatial structure, and reliability in fMRI models, addressing the following questions:
What is the relationship between prediction performance and model interpretation, specifically model reliability? We perform the first application of the Elastic Net sparse regression technique to fMRI data and find that reliability can be enhanced independently of prediction, particularly by accounting for the known spatial structure in the data.
How do we determine whether a model is reliable? We provide a novel argument that significance testing must be employed when evaluating model reliability, and introduce an evaluation approach that accounts for both the overall activity and spatial structure of a model, noticeably affecting reliability estimation and showing that model weight smoothing can improve reliability.
What are the spatial properties of the fMRI response? The Elastic Net models support the hypothesis that the fMRI spatial profile is characterized by distributed clusters of localized activity, and we extend the original framework beyond individual voxels to explore a much larger feature space of spatial clusters, demonstrating the importance of flexible modeling to accommodate the uncertainty of fMRI spatial structure.
How can one tractably produce sparse models in an enormous feature space, such as that of candidate fMRI spatial clusters? We introduce a distributed implementation of the LARS-EN algorithm for solving the Elastic Net, which can exploit a High Performance Computing environment to efficiently search such spaces.