10,175 research outputs found
Assessing the strength of directed influences among neural signals : An approach to noisy data
Acknowledgements This work was supported by the German Science Foundation (Ti315/4-2), the German Federal Ministry of Education and Research (BMBF grant 01GQ0420), and the Excellence Initiative of the German Federal and State Governments. B.S. is indebted to the Kosterlitz Centre for the financial support of this research project.Peer reviewedPreprin
High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity
Although the standard formulations of prediction problems involve
fully-observed and noiseless data drawn in an i.i.d. manner, many applications
involve noisy and/or missing data, possibly involving dependence, as well. We
study these issues in the context of high-dimensional sparse linear regression,
and propose novel estimators for the cases of noisy, missing and/or dependent
data. Many standard approaches to noisy or missing data, such as those using
the EM algorithm, lead to optimization problems that are inherently nonconvex,
and it is difficult to establish theoretical guarantees on practical
algorithms. While our approach also involves optimizing nonconvex programs, we
are able to both analyze the statistical error associated with any global
optimum, and more surprisingly, to prove that a simple algorithm based on
projected gradient descent will converge in polynomial time to a small
neighborhood of the set of all global minimizers. On the statistical side, we
provide nonasymptotic bounds that hold with high probability for the cases of
noisy, missing and/or dependent data. On the computational side, we prove that
under the same types of conditions required for statistical consistency, the
projected gradient descent algorithm is guaranteed to converge at a geometric
rate to a near-global minimizer. We illustrate these theoretical predictions
with simulations, showing close agreement with the predicted scalings.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1018 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Sparse Vector Autoregressive Modeling
The vector autoregressive (VAR) model has been widely used for modeling
temporal dependence in a multivariate time series. For large (and even
moderate) dimensions, the number of AR coefficients can be prohibitively large,
resulting in noisy estimates, unstable predictions and difficult-to-interpret
temporal dependence. To overcome such drawbacks, we propose a 2-stage approach
for fitting sparse VAR (sVAR) models in which many of the AR coefficients are
zero. The first stage selects non-zero AR coefficients based on an estimate of
the partial spectral coherence (PSC) together with the use of BIC. The PSC is
useful for quantifying the conditional relationship between marginal series in
a multivariate process. A refinement second stage is then applied to further
reduce the number of parameters. The performance of this 2-stage approach is
illustrated with simulation results. The 2-stage approach is also applied to
two real data examples: the first is the Google Flu Trends data and the second
is a time series of concentration levels of air pollutants.Comment: 39 pages, 7 figure
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
Measuring information-transfer delays
In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener’s principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics
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