Hypothesis Testing For Network Data in Functional Neuroimaging

Ginestet, Cedric E.; Li, Jun; Balachandran, Prakash; Rosenberg, Steven A.; Kolaczyk, Eric D.

doi:10.48550/arxiv.1407.5525

Cited by 3 publications

(5 citation statements)

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“…This work considers the scenario of observing M graphs, represented as adjacency matrices, A (1) , A (2) , . .…”

Section: Statistical Connectome Modelsmentioning

confidence: 99%

“…Input: Adjacency matrices A (1) , A (2) , For a given dimension d we consider the estimator lowrank d ( Ā) defined as the best rank-d positive-semidefinite approximation of Ā. Let Ŝ be a diagonal matrix with non-increasing entries along the diagonal corresponding to the largest d eigenvalues of Ā and let Û have columns given by the corresponding eigenvectors.…”

Section: Algorithm 2 Algorithm To Compute Pmentioning

confidence: 99%

“…In statistical connectomics, [2,3] propose a way to test if there is a difference between the distributions for two groups of networks. While hypothesis testing is the end goal of their work, estimation is a key intermediate step which may be improved by accounting for underlying structure in the mean matrix.…”

Section: Introductionmentioning

confidence: 99%

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Connectome smoothing via low-rank approximations

Tange

Ketcha

Badea

et al. 2019

IEEE Trans. Med. Imaging

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In brain imaging and connectomics, the study of brain networks, estimating the mean of a population of graphs based on a sample is a core problem. Often, this problem is especially difficult because the sample or cohort size is relatively small, sometimes even a single subject, while the number of nodes can be very large with noisy estimates of connectivity. While the element-wise sample mean of the adjacency matrices is a common approach, this method does not exploit underlying structural properties of the graphs. We propose using a low-rank method which incorporates dimension selection and diagonal augmentation to smooth the estimates and improve performance over the naïve methodology for small sample sizes. Theoretical results for the stochastic blockmodel show that this method offers major improvements when there are many vertices. Similarly, we demonstrate that the low-rank methods outperform the standard sample mean for a variety of independent edge distributions as well as human connectome data derived from magnetic resonance imaging, especially when sample sizes are small. Moreover, the low-rank methods yield "eigen-connectomes", which correlate with the lobe-structure of the human brain and superstructures of the mouse brain, and enable estimation of latent connectome structure. These results indicate that low-rank methods are an important part of the toolbox for researchers studying populations of graphs in general, and statistical connectomics in particular.

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“…This work considers the scenario of observing M graphs, represented as adjacency matrices, A (1) , A (2) , . .…”

Section: Statistical Connectome Modelsmentioning

confidence: 99%

Section: Algorithm 2 Algorithm To Compute Pmentioning

confidence: 99%

See 1 more Smart Citation

Connectome smoothing via low-rank approximations

Tange

Ketcha

Badea

et al. 2019

IEEE Trans. Med. Imaging

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show abstract

“…Multiple other methods have also been developed for quantifying differences across populations. Ginestet et al [2014] develop a central limit theorem for graph laplacians, allowing them to derive pivotal quantities and formally test for differences in pairs of networks. Zalesky, Fornito and Bullmore [2010] propose a network-based statistic to control the family-wise error rate when performing mass-univariate testing across all edges.…”

Section: Mixed Neighborhood Selectionmentioning

confidence: 99%

Learning population and subject-specific brain connectivity networks via mixed neighborhood selection

Monti¹,

Anagnostopoulos²,

Montana³

2017

Ann. Appl. Stat.

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In neuroimaging data analysis, Gaussian graphical models are often used to model statistical dependencies across spatially remote brain regions known as functional connectivity. Typically, data is collected across a cohort of subjects and the scientific objectives consist of estimating population and subject-specific graphical models. A third objective that is often overlooked involves quantifying intersubject variability and thus identifying regions or sub-networks that demonstrate heterogeneity across subjects. Such information is fundamental in order to thoroughly understand the human connectome. We propose Mixed Neighborhood Selection in order to simultaneously address the three aforementioned objectives. By recasting covariance selection as a neighborhood selection problem we are able to efficiently learn the topology of each node. We introduce an additional mixed effect component to neighborhood selection in order to simultaneously estimate a graphical model for the population of subjects as well as for each individual subject. The proposed method is validated empirically through a series of simulations and applied to resting state data for healthy subjects taken from the ABIDE consortium.

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“…In the general parametric framework, G ∼ f ∈ F = {f θ : θ ∈ Θ}, and selecting a principled and productive estimator θ for the unknown graph parameter θ given a sample of graphs {G (1) , • • • , G (m) } is one of the most foundational and essential tasks, facilitating subsequent inference. For example, Ginestet et al [2014] proposes a method to test for a difference between the networks of two groups of subjects in functional neuroimaging; while hypothesis testing is the ultimate goal, estimation is a key intermediate step. We propose a widely-applicable, robust, low-rank estimation procedure for a collection of weighted graphs.…”

Section: Background and Overviewmentioning

confidence: 99%

Robust Estimation from Multiple Graphs under Gross Error Contamination

Tang¹,

Tang²,

Vogelstein³

et al. 2017

Preprint

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Estimation of graph parameters based on a collection of graphs is essential for a wide range of graph inference tasks. In practice, weighted graphs are generally observed with edge contamination. We consider a weighted latent position graph model contaminated via an edge weight gross error model and propose an estimation methodology based on robust Lq estimation followed by low-rank adjacency spectral decomposition. We demonstrate that, under appropriate conditions, our estimator both maintains Lq robustness and wins the bias-variance tradeoff by exploiting lowrank graph structure. We illustrate the improvement offered by our estimator via both simulations and a human connectome data experiment.

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Hypothesis Testing For Network Data in Functional Neuroimaging

Cited by 3 publications

References 0 publications

Connectome smoothing via low-rank approximations

Connectome smoothing via low-rank approximations

Learning population and subject-specific brain connectivity networks via mixed neighborhood selection

Robust Estimation from Multiple Graphs under Gross Error Contamination

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