3,129 research outputs found
Adaptive Gaussian Markov Random Fields with Applications in Human Brain Mapping
Functional magnetic resonance imaging (fMRI) has become the standard technology in human brain mapping. Analyses of the massive spatio-temporal fMRI data sets often focus on parametric or nonparametric modeling of the temporal component, while spatial smoothing is based on Gaussian kernels or random fields. A weakness of Gaussian spatial smoothing is underestimation of activation peaks or blurring of high-curvature transitions between activated and non-activated brain regions. In this paper, we introduce a class of inhomogeneous Markov random fields (MRF) with spatially adaptive interaction weights in a space-varying coefficient model for fMRI data. For given weights, the random field is conditionally Gaussian, but marginally it is non-Gaussian. Fully Bayesian inference, including estimation of weights and variance parameters, is carried out through efficient MCMC simulation. An application to fMRI data from a visual stimulation experiment demonstrates the performance of our approach in comparison to Gaussian and robustified non-Gaussian Markov random field models
Physiological Gaussian Process Priors for the Hemodynamics in fMRI Analysis
Background: Inference from fMRI data faces the challenge that the hemodynamic
system that relates neural activity to the observed BOLD fMRI signal is
unknown.
New Method: We propose a new Bayesian model for task fMRI data with the
following features: (i) joint estimation of brain activity and the underlying
hemodynamics, (ii) the hemodynamics is modeled nonparametrically with a
Gaussian process (GP) prior guided by physiological information and (iii) the
predicted BOLD is not necessarily generated by a linear time-invariant (LTI)
system. We place a GP prior directly on the predicted BOLD response, rather
than on the hemodynamic response function as in previous literature. This
allows us to incorporate physiological information via the GP prior mean in a
flexible way, and simultaneously gives us the nonparametric flexibility of the
GP.
Results: Results on simulated data show that the proposed model is able to
discriminate between active and non-active voxels also when the GP prior
deviates from the true hemodynamics. Our model finds time varying dynamics when
applied to real fMRI data.
Comparison with Existing Method(s): The proposed model is better at detecting
activity in simulated data than standard models, without inflating the false
positive rate. When applied to real fMRI data, our GP model in several cases
finds brain activity where previously proposed LTI models does not.
Conclusions: We have proposed a new non-linear model for the hemodynamics in
task fMRI, that is able to detect active voxels, and gives the opportunity to
ask new kinds of questions related to hemodynamics.Comment: 18 pages, 14 figure
Spectral Characterization of functional MRI data on voxel-resolution cortical graphs
The human cortical layer exhibits a convoluted morphology that is unique to
each individual. Conventional volumetric fMRI processing schemes take for
granted the rich information provided by the underlying anatomy. We present a
method to study fMRI data on subject-specific cerebral hemisphere cortex (CHC)
graphs, which encode the cortical morphology at the resolution of voxels in
3-D. We study graph spectral energy metrics associated to fMRI data of 100
subjects from the Human Connectome Project database, across seven tasks.
Experimental results signify the strength of CHC graphs' Laplacian eigenvector
bases in capturing subtle spatial patterns specific to different functional
loads as well as experimental conditions within each task.Comment: Fixed two typos in the equations; (1) definition of L in section 2.1,
paragraph 1. (2) signal de-meaning and normalization in section 2.4,
paragraph
Interpretable statistics for complex modelling: quantile and topological learning
As the complexity of our data increased exponentially in the last decades, so has our
need for interpretable features. This thesis revolves around two paradigms to approach
this quest for insights.
In the first part we focus on parametric models, where the problem of interpretability
can be seen as a “parametrization selection”. We introduce a quantile-centric
parametrization and we show the advantages of our proposal in the context of regression,
where it allows to bridge the gap between classical generalized linear (mixed)
models and increasingly popular quantile methods.
The second part of the thesis, concerned with topological learning, tackles the
problem from a non-parametric perspective. As topology can be thought of as a way
of characterizing data in terms of their connectivity structure, it allows to represent
complex and possibly high dimensional through few features, such as the number of
connected components, loops and voids. We illustrate how the emerging branch of
statistics devoted to recovering topological structures in the data, Topological Data
Analysis, can be exploited both for exploratory and inferential purposes with a special
emphasis on kernels that preserve the topological information in the data.
Finally, we show with an application how these two approaches can borrow strength
from one another in the identification and description of brain activity through fMRI
data from the ABIDE project
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