30,014 research outputs found
Algorithms of causal inference for the analysis of effective connectivity among brain regions
In recent years, powerful general algorithms of causal inference have been developed. In particular, in the framework of Pearl’s causality, algorithms of inductive causation (IC and IC*) provide a procedure to determine which causal connections among nodes in a network can be inferred from empirical observations even in the presence of latent variables, indicating the limits of what can be learned without active manipulation of the system. These algorithms can in principle become important complements to established techniques such as Granger causality and Dynamic Causal Modeling (DCM) to analyze causal influences (effective connectivity) among brain regions. However, their application to dynamic processes has not been yet examined. Here we study how to apply these algorithms to time-varying signals such as electrophysiological or neuroimaging signals. We propose a new algorithm which combines the basic principles of the previous algorithms with Granger causality to obtain a representation of the causal relations suited to dynamic processes. Furthermore, we use graphical criteria to predict dynamic statistical dependencies between the signals from the causal structure. We show how some problems for causal inference from neural signals (e.g., measurement noise, hemodynamic responses, and time aggregation) can be understood in a general graphical approach. Focusing on the effect of spatial aggregation, we show that when causal inference is performed at a coarser scale than the one at which the neural sources interact, results strongly depend on the degree of integration of the neural sources aggregated in the signals, and thus characterize more the intra-areal properties than the interactions among regions. We finally discuss how the explicit consideration of latent processes contributes to understand Granger causality and DCM as well as to distinguish functional and effective connectivity
Towards a Multi-Subject Analysis of Neural Connectivity
Directed acyclic graphs (DAGs) and associated probability models are widely
used to model neural connectivity and communication channels. In many
experiments, data are collected from multiple subjects whose connectivities may
differ but are likely to share many features. In such circumstances it is
natural to leverage similarity between subjects to improve statistical
efficiency. The first exact algorithm for estimation of multiple related DAGs
was recently proposed by Oates et al. 2014; in this letter we present examples
and discuss implications of the methodology as applied to the analysis of fMRI
data from a multi-subject experiment. Elicitation of tuning parameters requires
care and we illustrate how this may proceed retrospectively based on technical
replicate data. In addition to joint learning of subject-specific connectivity,
we allow for heterogeneous collections of subjects and simultaneously estimate
relationships between the subjects themselves. This letter aims to highlight
the potential for exact estimation in the multi-subject setting.Comment: to appear in Neural Computation 27:1-2
Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches
In the past two decades, functional Magnetic Resonance Imaging has been used
to relate neuronal network activity to cognitive processing and behaviour.
Recently this approach has been augmented by algorithms that allow us to infer
causal links between component populations of neuronal networks. Multiple
inference procedures have been proposed to approach this research question but
so far, each method has limitations when it comes to establishing whole-brain
connectivity patterns. In this work, we discuss eight ways to infer causality
in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality,
Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and
Transfer Entropy. We finish with formulating some recommendations for the
future directions in this area
Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?
Correlations in the signal observed via functional Magnetic Resonance Imaging
(fMRI), are expected to reveal the interactions in the underlying neural
populations through hemodynamic response. In particular, they highlight
distributed set of mutually correlated regions that correspond to brain
networks related to different cognitive functions. Yet graph-theoretical
studies of neural connections give a different picture: that of a highly
integrated system with small-world properties: local clustering but with short
pathways across the complete structure. We examine the conditional independence
properties of the fMRI signal, i.e. its Markov structure, to find realistic
assumptions on the connectivity structure that are required to explain the
observed functional connectivity. In particular we seek a decomposition of the
Markov structure into segregated functional networks using decomposable graphs:
a set of strongly-connected and partially overlapping cliques. We introduce a
new method to efficiently extract such cliques on a large, strongly-connected
graph. We compare methods learning different graph structures from functional
connectivity by testing the goodness of fit of the model they learn on new
data. We find that summarizing the structure as strongly-connected networks can
give a good description only for very large and overlapping networks. These
results highlight that Markov models are good tools to identify the structure
of brain connectivity from fMRI signals, but for this purpose they must reflect
the small-world properties of the underlying neural systems
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
Learning and comparing functional connectomes across subjects
Functional connectomes capture brain interactions via synchronized
fluctuations in the functional magnetic resonance imaging signal. If measured
during rest, they map the intrinsic functional architecture of the brain. With
task-driven experiments they represent integration mechanisms between
specialized brain areas. Analyzing their variability across subjects and
conditions can reveal markers of brain pathologies and mechanisms underlying
cognition. Methods of estimating functional connectomes from the imaging signal
have undergone rapid developments and the literature is full of diverse
strategies for comparing them. This review aims to clarify links across
functional-connectivity methods as well as to expose different steps to perform
a group study of functional connectomes
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