Gaussian Naive Bayes with Smooth Basis Functions

We examine advantages of using smooth basis functions in classifying fMRI (functional MR Imaging) data. fMRI data is a measurement of neural activity in the brain. It allows us to see how each part of the brain responses to stimuli. The task in which we are interested is to identify mental states from some given fMRI data. Specifically, we want to classify between two different states using labeled data. There are two main challenges for this task. First, fMRI data is very noisy and high-dimensional. Second, we only have limited amount of training data. One of the traditional ways is to use Gaussian Naive Bayes (GNB) classifier. The Naive part means we assume that each data point, i.e. activation at each voxel at each time point, is independent. The Gaussian part means we also assume that each data point is drawn from a normal distribution with parameters, μ and σ. Technically, fMRI measures changes in the blood oxygenation level, also known as hemodynamic response (HR) which is an indirect correlate of neural activity in the brain. The hemodynamic response to a stimulus can last some period of time. Therefore, it makes sense to believe that fMRI data is composed of many HRs fired at different times. Since the HR is simply blood flow, we should be able to model each HR with a smooth function over time. Consequently, this idea suggests us that we should be able model fMRI data using composition of smooth functions. In this thesis, we modify the traditional GNB so that, instead of learning μ at each time point independently, we learn weights of smooth basis functions and calculate μ accordingly. Furthermore, by doing so, it allows