Bayesian kernel methods for analysis of functional neuroimages

The relevance sample-feature machine: a sparse Bayesian learning approach to joint feature-sample selection

This paper introduces a novel sparse Bayesian machine-learning algorithm for embedded feature selection in classification tasks. Our proposed algorithm, called the relevance sample feature machine (RSFM), is able to simultaneously choose the relevance samples and also the relevance features for regression or classification problems. We propose a separable model in feature and sample domains. Adopting a Bayesian approach and using Gaussian priors, the learned model by RSFM is sparse in both sample and feature domains. The proposed algorithm is an extension of the standard RVM algorithm, which only opts for sparsity in the sample domain. Experimental comparisons on synthetic as well as benchmark data sets show that RSFM is successful in both feature selection (eliminating the irrelevant features) and accurate classification. The main advantages of our proposed algorithm are: less system complexity, better generalization and avoiding overfitting, and less computational cost during the testing stage.

A sparse and spatially constrained generative regression model for fMRI data analysis

In this study, we present an advanced Bayesian framework for the analysis of functional magnetic resonance imaging (fMRI) data that simultaneously employs both spatial and sparse properties. The basic building block of our method is the general linear regression model that constitutes a well-known probabilistic approach. By treating regression coefficients as random variables, we can apply an enhanced Gibbs distribution function that captures spatial constrains and at the same time allows sparse representation of fMRI time series. The proposed scheme is described as a maximum a posteriori approach, where the known expectation maximization algorithm is applied offering closed-form update equations for the model parameters. We have demonstrated that our method produces improved performance and functional activation detection capabilities in both simulated data and real applications.

Shifting from region of interest (ROI) to voxel-based analysis in human brain mapping

Current clinical studies involve multidimensional high-resolution images containing an overwhelming amount of structural and functional information. The analysis of such a wealth of information is becoming increasingly difficult yet necessary in order to improve diagnosis, treatment and healthcare. Voxel-wise analysis is a class of modern methods of image processing in the medical field with increased popularity. It has replaced manual region of interest (ROI) analysis and has provided tools to make statistical inferences at voxel level. The introduction of voxel-based analysis software in all modern commercial scanners allows clinical use of these techniques. This review will explain the main principles, advantages and disadvantages behind these methods of image analysis.

Comparing Classification Methods for Longitudinal fMRI Studies

We compare 10 methods of classifying fMRI volumes by applying them to data from a longitudinal study of stroke recovery: adaptive Fisher's linear and quadratic discriminant; gaussian naive Bayes; support vector machines with linear, quadratic, and radial basis function (RBF) kernels; logistic regression; two novel methods based on pairs of restricted Boltzmann machines (RBM); and K-nearest neighbors. All methods were tested on three binary classification tasks, and their out-of-sample classification accuracies are compared. The relative performance of the methods varies considerably across subjects and classification tasks. The best overall performers were adaptive quadratic discriminant, support vector machines with RBF kernels, and generatively trained pairs of RBMs.

Modeling inter-subject variability in FMRI activation location: a Bayesian hierarchical spatial model

The aim of this article is to develop a spatial model for multi-subject fMRI data. There has been extensive work on univariate modeling of each voxel for single and multi-subject data, some work on spatial modeling of single-subject data, and some recent work on spatial modeling of multi-subject data. However, there has been no work on spatial models that explicitly account for inter-subject variability in activation locations. In this article, we use the idea of activation centers and model the inter-subject variability in activation locations directly. Our model is specified in a Bayesian hierarchical framework which allows us to draw inferences at all levels: the population level, the individual level, and the voxel level. We use Gaussian mixtures for the probability that an individual has a particular activation. This helps answer an important question that is not addressed by any of the previous methods: What proportion of subjects had a significant activity in a given region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov chain Monte Carlo. We demonstrate our method with a fMRI study of resolving proactive interference and show dramatically better precision of localization with our method relative to the standard mass-univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data.

Activated region fitting: a robust high-power method for fMRI analysis using parameterized regions of activation

An important issue in the analysis of fMRI is how to account for the spatial smoothness of activated regions. In this article a method is proposed to accomplish this by modeling activated regions with Gaussian shapes. Hypothesis tests on the location, spatial extent, and amplitude of these regions are performed instead of hypothesis tests of individual voxels. This increases power and eases interpretation. Simulation studies show robust hypothesis tests under misspecification of the shape model, and increased power over standard techniques especially at low signal-to-noise ratios. An application to real single-subject data also indicates that the method has increased power over standard methods.

Sparse Bayesian modeling with adaptive kernel learning

Sparse kernel methods are very efficient in solving regression and classification problems. The sparsity and performance of these methods depend on selecting an appropriate kernel function, which is typically achieved using a cross-validation procedure. In this paper, we propose an incremental method for supervised learning, which is similar to the relevance vector machine (RVM) but also learns the parameters of the kernels during model training. Specifically, we learn different parameter values for each kernel, resulting in a very flexible model. In order to avoid overfitting, we use a sparsity enforcing prior that controls the effective number of parameters of the model. We present experimental results on artificial data to demonstrate the advantages of the proposed method and we provide a comparison with the typical RVM on several commonly used regression and classification data sets.