2,021 research outputs found
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Modeling High-Dimensional Multichannel Brain Signals
Our goal is to model and measure functional and effective (directional) connectivity in multichannel brain physiological signals (e.g., electroencephalograms, local field potentials). The difficulties from analyzing these data mainly come from two aspects: first, there are major statistical and computational challenges for modeling and analyzing high-dimensional multichannel brain signals; second, there is no set of universally agreed measures for characterizing connectivity. To model multichannel brain signals, our approach is to fit a vector autoregressive (VAR) model with potentially high lag order so that complex lead-lag temporal dynamics between the channels can be captured. Estimates of the VAR model will be obtained by our proposed hybrid LASSLE (LASSO + LSE) method which combines regularization (to control for sparsity) and least squares estimation (to improve bias and mean-squared error). Then we employ some measures of connectivity but put an emphasis on partial directed coherence (PDC) which can capture the directional connectivity between channels. PDC is a frequency-specific measure that explains the extent to which the present oscillatory activity in a sender channel influences the future oscillatory activity in a specific receiver channel relative to all possible receivers in the network. The proposed modeling approach provided key insights into potential functional relationships among simultaneously recorded sites during performance of a complex memory task. Specifically, this novel method was successful in quantifying patterns of effective connectivity across electrode locations, and in capturing how these patterns varied across trial epochs and trial types
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On Nonregularized Estimation of Psychological Networks.
An important goal for psychological science is developing methods to characterize relationships between variables. Customary approaches use structural equation models to connect latent factors to a number of observed measurements, or test causal hypotheses between observed variables. More recently, regularized partial correlation networks have been proposed as an alternative approach for characterizing relationships among variables through off-diagonal elements in the precision matrix. While the graphical Lasso (glasso) has emerged as the default network estimation method, it was optimized in fields outside of psychology with very different needs, such as high dimensional data where the number of variables (p) exceeds the number of observations (n). In this article, we describe the glasso method in the context of the fields where it was developed, and then we demonstrate that the advantages of regularization diminish in settings where psychological networks are often fitted ( p≪n ). We first show that improved properties of the precision matrix, such as eigenvalue estimation, and predictive accuracy with cross-validation are not always appreciable. We then introduce nonregularized methods based on multiple regression and a nonparametric bootstrap strategy, after which we characterize performance with extensive simulations. Our results demonstrate that the nonregularized methods can be used to reduce the false-positive rate, compared to glasso, and they appear to provide consistent performance across sparsity levels, sample composition (p/n), and partial correlation size. We end by reviewing recent findings in the statistics literature that suggest alternative methods often have superior performance than glasso, as well as suggesting areas for future research in psychology. The nonregularized methods have been implemented in the R package GGMnonreg
Computational Models for Transplant Biomarker Discovery.
Translational medicine offers a rich promise for improved diagnostics and drug discovery for biomedical research in the field of transplantation, where continued unmet diagnostic and therapeutic needs persist. Current advent of genomics and proteomics profiling called "omics" provides new resources to develop novel biomarkers for clinical routine. Establishing such a marker system heavily depends on appropriate applications of computational algorithms and software, which are basically based on mathematical theories and models. Understanding these theories would help to apply appropriate algorithms to ensure biomarker systems successful. Here, we review the key advances in theories and mathematical models relevant to transplant biomarker developments. Advantages and limitations inherent inside these models are discussed. The principles of key -computational approaches for selecting efficiently the best subset of biomarkers from high--dimensional omics data are highlighted. Prediction models are also introduced, and the integration of multi-microarray data is also discussed. Appreciating these key advances would help to accelerate the development of clinically reliable biomarker systems
Hemodynamic Deconvolution Demystified: Sparsity-Driven Regularization at Work
Deconvolution of the hemodynamic response is an important step to access
short timescales of brain activity recorded by functional magnetic resonance
imaging (fMRI). Albeit conventional deconvolution algorithms have been around
for a long time (e.g., Wiener deconvolution), recent state-of-the-art methods
based on sparsity-pursuing regularization are attracting increasing interest to
investigate brain dynamics and connectivity with fMRI. This technical note
revisits the main concepts underlying two main methods, Paradigm Free Mapping
and Total Activation, in the most accessible way. Despite their apparent
differences in the formulation, these methods are theoretically equivalent as
they represent the synthesis and analysis sides of the same problem,
respectively. We demonstrate this equivalence in practice with their
best-available implementations using both simulations, with different
signal-to-noise ratios, and experimental fMRI data acquired during a motor task
and resting-state. We evaluate the parameter settings that lead to equivalent
results, and showcase the potential of these algorithms compared to other
common approaches. This note is useful for practitioners interested in gaining
a better understanding of state-of-the-art hemodynamic deconvolution, and aims
to answer questions that practitioners often have regarding the differences
between the two methods.Comment: 18 pages, 6 figures, submitted to Apertur
Information Transfer in Linear Multivariate Processes Assessed through Penalized Regression Techniques: Validation and Application to Physiological Networks
The framework of information dynamics allows the dissection of the information processed
in a network of multiple interacting dynamical systems into meaningful elements of computation
that quantify the information generated in a target system, stored in it, transferred to it from one or
more source systems, and modified in a synergistic or redundant way. The concepts of information
transfer and modification have been recently formulated in the context of linear parametric modeling
of vector stochastic processes, linking them to the notion of Granger causality and providing efficient
tools for their computation based on the state–space (SS) representation of vector autoregressive
(VAR) models. Despite their high computational reliability these tools still suffer from estimation
problems which emerge, in the case of low ratio between data points available and the number of
time series, when VAR identification is performed via the standard ordinary least squares (OLS).
In this work we propose to replace the OLS with penalized regression performed through the
Least Absolute Shrinkage and Selection Operator (LASSO), prior to computation of the measures of
information transfer and information modification. First, simulating networks of several coupled
Gaussian systems with complex interactions, we show that the LASSO regression allows, also in
conditions of data paucity, to accurately reconstruct both the underlying network topology and the
expected patterns of information transfer. Then we apply the proposed VAR-SS-LASSO approach to
a challenging application context, i.e., the study of the physiological network of brain and peripheral
interactions probed in humans under different conditions of rest and mental stress. Our results,
which document the possibility to extract physiologically plausible patterns of interaction between
the cardiovascular, respiratory and brain wave amplitudes, open the way to the use of our new
analysis tools to explore the emerging field of Network Physiology in several practical applications
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