29,071 research outputs found
Estimating Time-Varying Effective Connectivity in High-Dimensional fMRI Data Using Regime-Switching Factor Models
Recent studies on analyzing dynamic brain connectivity rely on sliding-window
analysis or time-varying coefficient models which are unable to capture both
smooth and abrupt changes simultaneously. Emerging evidence suggests
state-related changes in brain connectivity where dependence structure
alternates between a finite number of latent states or regimes. Another
challenge is inference of full-brain networks with large number of nodes. We
employ a Markov-switching dynamic factor model in which the state-driven
time-varying connectivity regimes of high-dimensional fMRI data are
characterized by lower-dimensional common latent factors, following a
regime-switching process. It enables a reliable, data-adaptive estimation of
change-points of connectivity regimes and the massive dependencies associated
with each regime. We consider the switching VAR to quantity the dynamic
effective connectivity. We propose a three-step estimation procedure: (1)
extracting the factors using principal component analysis (PCA) and (2)
identifying dynamic connectivity states using the factor-based switching vector
autoregressive (VAR) models in a state-space formulation using Kalman filter
and expectation-maximization (EM) algorithm, and (3) constructing the
high-dimensional connectivity metrics for each state based on subspace
estimates. Simulation results show that our proposed estimator outperforms the
K-means clustering of time-windowed coefficients, providing more accurate
estimation of regime dynamics and connectivity metrics in high-dimensional
settings. Applications to analyzing resting-state fMRI data identify dynamic
changes in brain states during rest, and reveal distinct directed connectivity
patterns and modular organization in resting-state networks across different
states.Comment: 21 page
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
Distributed state estimation in sensor networks with randomly occurring nonlinearities subject to time delays
This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 ACM.This article is concerned with a new distributed state estimation problem for a class of dynamical systems in sensor networks. The target plant is described by a set of differential equations disturbed by a Brownian motion and randomly occurring nonlinearities (RONs) subject to time delays. The RONs are investigated here to reflect network-induced randomly occurring regulation of the delayed states on the current ones. Through available measurement output transmitted from the sensors, a distributed state estimator is designed to estimate the states of the target system, where each sensor can communicate with the neighboring sensors according to the given topology by means of a directed graph. The state estimation is carried out in a distributed way and is therefore applicable to online application. By resorting to the Lyapunov functional combined with stochastic analysis techniques, several delay-dependent criteria are established that not only ensure the estimation error to be globally asymptotically stable in the mean square, but also guarantee the existence of the desired estimator gains that can then be explicitly expressed when certain matrix inequalities are solved. A numerical example is given to verify the designed distributed state estimators.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60804028 and 61174136, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK,
and the Alexander von Humboldt Foundation of Germany
Estimating the Spot Covariation of Asset Prices - Statistical Theory and Empirical Evidence
We propose a new estimator for the spot covariance matrix of a
multi-dimensional continuous semi-martingale log asset price process which is
subject to noise and non-synchronous observations. The estimator is constructed
based on a local average of block-wise parametric spectral covariance
estimates. The latter originate from a local method of moments (LMM) which
recently has been introduced. We prove consistency and a point-wise stable
central limit theorem for the proposed spot covariance estimator in a very
general setup with stochastic volatility, leverage effects and general noise
distributions. Moreover, we extend the LMM estimator to be robust against
autocorrelated noise and propose a method to adaptively infer the
autocorrelations from the data. Based on simulations we provide empirical
guidance on the effective implementation of the estimator and apply it to
high-frequency data of a cross-section of Nasdaq blue chip stocks. Employing
the estimator to estimate spot covariances, correlations and volatilities in
normal but also unusual periods yields novel insights into intraday covariance
and correlation dynamics. We show that intraday (co-)variations (i) follow
underlying periodicity patterns, (ii) reveal substantial intraday variability
associated with (co-)variation risk, and (iii) can increase strongly and nearly
instantaneously if new information arrives
High dimensional Sparse Gaussian Graphical Mixture Model
This paper considers the problem of networks reconstruction from
heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well
known that parameter estimation in this context is challenging due to large
numbers of variables coupled with the degeneracy of the likelihood. We propose
as a solution a penalized maximum likelihood technique by imposing an
penalty on the precision matrix. Our approach shrinks the parameters thereby
resulting in better identifiability and variable selection. We use the
Expectation Maximization (EM) algorithm which involves the graphical LASSO to
estimate the mixing coefficients and the precision matrices. We show that under
certain regularity conditions the Penalized Maximum Likelihood (PML) estimates
are consistent. We demonstrate the performance of the PML estimator through
simulations and we show the utility of our method for high dimensional data
analysis in a genomic application
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