7,050 research outputs found
The generalized shrinkage estimator for the analysis of functional connectivity of brain signals
We develop a new statistical method for estimating functional connectivity
between neurophysiological signals represented by a multivariate time series.
We use partial coherence as the measure of functional connectivity. Partial
coherence identifies the frequency bands that drive the direct linear
association between any pair of channels. To estimate partial coherence, one
would first need an estimate of the spectral density matrix of the multivariate
time series. Parametric estimators of the spectral density matrix provide good
frequency resolution but could be sensitive when the parametric model is
misspecified. Smoothing-based nonparametric estimators are robust to model
misspecification and are consistent but may have poor frequency resolution. In
this work, we develop the generalized shrinkage estimator, which is a weighted
average of a parametric estimator and a nonparametric estimator. The optimal
weights are frequency-specific and derived under the quadratic risk criterion
so that the estimator, either the parametric estimator or the nonparametric
estimator, that performs better at a particular frequency receives heavier
weight. We validate the proposed estimator in a simulation study and apply it
on electroencephalogram recordings from a visual-motor experiment.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS396 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Neural Connectivity with Hidden Gaussian Graphical State-Model
The noninvasive procedures for neural connectivity are under questioning.
Theoretical models sustain that the electromagnetic field registered at
external sensors is elicited by currents at neural space. Nevertheless, what we
observe at the sensor space is a superposition of projected fields, from the
whole gray-matter. This is the reason for a major pitfall of noninvasive
Electrophysiology methods: distorted reconstruction of neural activity and its
connectivity or leakage. It has been proven that current methods produce
incorrect connectomes. Somewhat related to the incorrect connectivity
modelling, they disregard either Systems Theory and Bayesian Information
Theory. We introduce a new formalism that attains for it, Hidden Gaussian
Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM) hidden
by the observation equation of Magneto-encephalographic (MEEG) signals. HIGGS
is equivalent to a frequency domain Linear State Space Model (LSSM) but with
sparse connectivity prior. The mathematical contribution here is the theory for
high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS
can attenuate the leakage effect in the most critical case: the distortion EEG
signal due to head volume conduction heterogeneities. Its application in EEG is
illustrated with retrieved connectivity patterns from human Steady State Visual
Evoked Potentials (SSVEP). We provide for the first time confirmatory evidence
for noninvasive procedures of neural connectivity: concurrent EEG and
Electrocorticography (ECoG) recordings on monkey. Open source packages are
freely available online, to reproduce the results presented in this paper and
to analyze external MEEG databases
Adaptive nonlinear multivariate brain connectivity analysis of motor imagery movements using graph theory
Recent studies on motor imagery (MI)-based brain computer interaction (BCI) reported that the interaction of spatially separated brain areas in forms of functional or effective connectivity leads to a better insight of brain neural patterns during MI movements and can provide useful features for BCIs. However, existing studies suffer from unrealistic assumptions or technical weaknesses for processing brain signals, such as stationarity, linearity and bivariate analysis framework. Besides, volume conduction effect as a critical challenge in this area and the role of subcortical regions in connectivity analysis have not been considered and studied well. In this thesis, the neurophysiological connectivity patterns of healthy human brain during different MI movements are deeply investigated. At first, an adaptive nonlinear multivariate statespace model known as dual extended Kalman filter is proposed for connectivity pattern estimation. Several frequency domain functional and effective connectivity estimators are developed for nonlinear non-stationary signals. Evaluation results show superior parameter tracking performance and hence more accurate connectivity analysis by the proposed model. Secondly, source-space time-varying nonlinear multivariate brain connectivity during feet, left hand, right hand and tongue MI movements is investigated in a broad frequency range by using the developed connectivity estimators. Results reveal the similarities and the differences between MI tasks in terms of involved regions, density of interactions, distribution of interactions, functional connections and information flows. Finally, organizational principles of brain networks of MI movements measured by all considered connectivity estimators are extensively explored by graph theoretical approach where the local and global graph structures are quantified by computing different graph indexes. Results report statistical significant differences between and within the MI tasks by using the graph indexes extracted from the networks formed particularly by normalized partial directed coherence. This delivers promising distinctive features of the MI tasks for non-invasive BCI applications
Mutual Information in Frequency and its Application to Measure Cross-Frequency Coupling in Epilepsy
We define a metric, mutual information in frequency (MI-in-frequency), to
detect and quantify the statistical dependence between different frequency
components in the data, referred to as cross-frequency coupling and apply it to
electrophysiological recordings from the brain to infer cross-frequency
coupling. The current metrics used to quantify the cross-frequency coupling in
neuroscience cannot detect if two frequency components in non-Gaussian brain
recordings are statistically independent or not. Our MI-in-frequency metric,
based on Shannon's mutual information between the Cramer's representation of
stochastic processes, overcomes this shortcoming and can detect statistical
dependence in frequency between non-Gaussian signals. We then describe two
data-driven estimators of MI-in-frequency: one based on kernel density
estimation and the other based on the nearest neighbor algorithm and validate
their performance on simulated data. We then use MI-in-frequency to estimate
mutual information between two data streams that are dependent across time,
without making any parametric model assumptions. Finally, we use the MI-in-
frequency metric to investigate the cross-frequency coupling in seizure onset
zone from electrocorticographic recordings during seizures. The inferred
cross-frequency coupling characteristics are essential to optimize the spatial
and spectral parameters of electrical stimulation based treatments of epilepsy.Comment: This paper is accepted for publication in IEEE Transactions on Signal
Processing and contains 15 pages, 9 figures and 1 tabl
The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference
Background: Wiener-Granger causality (“G-causality”) is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling.
New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy.
Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference.
Comparison with Existing Method(s): The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain.
Conclusions: The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference.
Keywords: Granger causality, vector autoregressive modelling, time series analysi
Machine Learning for Neuroimaging with Scikit-Learn
Statistical machine learning methods are increasingly used for neuroimaging
data analysis. Their main virtue is their ability to model high-dimensional
datasets, e.g. multivariate analysis of activation images or resting-state time
series. Supervised learning is typically used in decoding or encoding settings
to relate brain images to behavioral or clinical observations, while
unsupervised learning can uncover hidden structures in sets of images (e.g.
resting state functional MRI) or find sub-populations in large cohorts. By
considering different functional neuroimaging applications, we illustrate how
scikit-learn, a Python machine learning library, can be used to perform some
key analysis steps. Scikit-learn contains a very large set of statistical
learning algorithms, both supervised and unsupervised, and its application to
neuroimaging data provides a versatile tool to study the brain.Comment: Frontiers in neuroscience, Frontiers Research Foundation, 2013, pp.1
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