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25
Causal Network Inference via Group Sparse Regularization
"... This paper addresses the problem of inferring sparse causal networks modeled by multivariate autoregressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a “false connection score ” ..."
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This paper addresses the problem of inferring sparse causal networks modeled by multivariate autoregressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a “false connection score ” ψ. In particular, we show that consistent recovery is possible even when the number of observations of the network is far less than the number of parameters describing the network, provided that ψ < 1. The false connection score is also demonstrated to be a useful metric of recovery in nonasymptotic regimes. The conditions suggest a modified gLasso procedure which tends to improve the false connection score and reduce the chances of reversing the direction of causal influence. Computational experiments and a real network based electrocorticogram (ECoG) simulation study demonstrate the effectiveness of the approach.
Modeling sparse connectivity between underlying brain sources for EEG/MEG
, 2010
"... We propose a novel technique to assess functional brain connectivity in eletro/magnetoencephalographic (EEG/MEG) signals. Our method, called SparselyConnected Sources Analysis (SCSA), can overcome the problem of volume conduction by modeling neural data innovatively with the following ingredients: ..."
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We propose a novel technique to assess functional brain connectivity in eletro/magnetoencephalographic (EEG/MEG) signals. Our method, called SparselyConnected Sources Analysis (SCSA), can overcome the problem of volume conduction by modeling neural data innovatively with the following ingredients: (a) the EEG/MEG is assumed to be a linear mixture of correlated sources following a multivariate autoregressive (MVAR) model, (b) the demixing is estimated jointly with the source MVAR parameters, (c) overfitting is avoided by using the Group Lasso penalty. This approach allows us to extract the appropriate level of crosstalk between the extracted sources and in this manner we obtain a sparse datadriven model of functional connectivity. We demonstrate the usefulness of SCSA with simulated data, and compare it to a number of existing algorithms with excellent results. 1
Sparse Causal Discovery in Multivariate Time Series
, 2008
"... Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on nonvanishing coefficients belonging to respective timelagged instances. As in most cases a parsimonious causality structure is assumed, a promising appro ..."
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Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on nonvanishing coefficients belonging to respective timelagged instances. As in most cases a parsimonious causality structure is assumed, a promising approach to causal discovery consists in fitting VAR models with an additional sparsitypromoting regularization. Along this line we here propose that sparsity should be enforced for the subgroups of coefficients that belong to each pair of time series, as the absence of a causal relation requires the coefficients for all timelags to become jointly zero. Such behavior can be achieved by means of ℓ1,2norm regularized regression, for which an efficient active set solver has been proposed recently. Our method is shown to outperform standard methods in recovering simulated causality graphs. The results are on par with a second novel approach which uses multiple statistical testing.
Bayesian Source Localization with the Multivariate Laplace Prior
"... We introduce a novel multivariate Laplace (MVL) distribution as a sparsity promoting prior for Bayesian source localization that allows the specification of constraints between and within sources. We represent the MVL distribution as a scale mixture that induces a coupling between source variances i ..."
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We introduce a novel multivariate Laplace (MVL) distribution as a sparsity promoting prior for Bayesian source localization that allows the specification of constraints between and within sources. We represent the MVL distribution as a scale mixture that induces a coupling between source variances instead of their means. Approximation of the posterior marginals using expectation propagation is shown to be very efficient due to properties of the scale mixture representation. The computational bottleneck amounts to computing the diagonal elements of a sparse matrix inverse. Our approach is illustrated using a mismatch negativity paradigm for which MEG data and a structural MRI have been acquired. We show that spatial coupling leads to sources which are active over larger cortical areas as compared with an uncoupled prior. 1
Timefrequency mixednorm estimates: Sparse M/EEG imaging with nonstationary source activations
 NeuroImage
, 2013
"... Magnetoencephalography (MEG) and electroencephalography (EEG) allow functional brain imaging with high temporal resolution. While solving the inverse problem independently at every time point can give an image of the active brain at every millisecond, such a procedure does not capitalize on the tem ..."
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Cited by 7 (0 self)
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Magnetoencephalography (MEG) and electroencephalography (EEG) allow functional brain imaging with high temporal resolution. While solving the inverse problem independently at every time point can give an image of the active brain at every millisecond, such a procedure does not capitalize on the temporal dynamics of the signal. Linear inverse methods (Minimumnorm, dSPM, sLORETA, beamformers) typically assume that the signal is stationary: regularization parameter and data covariance are independent of time and the time varying signaltonoise ratio (SNR). Other recently proposed nonlinear inverse solvers promoting focal activations estimate the sources in both space and time while also assuming stationary sources during a time interval. However such an hypothesis only holds for short time intervals. To overcome this limitation, we propose timefrequency mixednorm estimates (TFMxNE), which use timefrequency analysis to regularize the illposed inverse problem. This method makes use of structured sparse priors
Estimating vector fields using sparse basis field expansions
, 2009
"... We introduce a novel framework for estimating vector fields using sparse basis field expansions (SFLEX). The notion of basis fields, which are an extension of scalar basis functions, arises naturally in our framework from a rotational invariance requirement. We consider a regression setting as well ..."
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We introduce a novel framework for estimating vector fields using sparse basis field expansions (SFLEX). The notion of basis fields, which are an extension of scalar basis functions, arises naturally in our framework from a rotational invariance requirement. We consider a regression setting as well as inverse problems. All variants discussed lead to secondorder cone programming formulations. While our framework is generally applicable to any type of vector field, we focus in this paper on applying it to solving the EEG/MEG inverse problem. It is shown that significantly more precise and neurophysiologically more plausible location and shape estimates of cerebral current sources from EEG/MEG measurements become possible with our method when comparing to the stateoftheart.
Combined classification and channel/basis selection with L1L2 regularization with application to P300 speller system
 In Proceedings of the 4th International BrainComputer Interface Workshop and Training Course 2008. Verlag der Technischen Universität Graz
, 2008
"... regularization with application to P300 speller system ..."
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regularization with application to P300 speller system
Open Database of Epileptic EEG with MRI and Postoperational Assessment of Foci—a Real World Verification for the EEG Inverse Solutions
, 2010
"... © The Author(s) 2010. This article is published with open access at Springerlink.com Abstract This paper introduces a freely accessible database ..."
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© The Author(s) 2010. This article is published with open access at Springerlink.com Abstract This paper introduces a freely accessible database
and Postoperational Assessment of Foci—a Real World Verification for the EEG Inverse Solutions
, 2010
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.