79,695 research outputs found
Estimating mutual information and multi--information in large networks
We address the practical problems of estimating the information relations
that characterize large networks. Building on methods developed for analysis of
the neural code, we show that reliable estimates of mutual information can be
obtained with manageable computational effort. The same methods allow
estimation of higher order, multi--information terms. These ideas are
illustrated by analyses of gene expression, financial markets, and consumer
preferences. In each case, information theoretic measures correlate with
independent, intuitive measures of the underlying structures in the system
Equitability, mutual information, and the maximal information coefficient
Reshef et al. recently proposed a new statistical measure, the "maximal
information coefficient" (MIC), for quantifying arbitrary dependencies between
pairs of stochastic quantities. MIC is based on mutual information, a
fundamental quantity in information theory that is widely understood to serve
this need. MIC, however, is not an estimate of mutual information. Indeed, it
was claimed that MIC possesses a desirable mathematical property called
"equitability" that mutual information lacks. This was not proven; instead it
was argued solely through the analysis of simulated data. Here we show that
this claim, in fact, is incorrect. First we offer mathematical proof that no
(non-trivial) dependence measure satisfies the definition of equitability
proposed by Reshef et al.. We then propose a self-consistent and more general
definition of equitability that follows naturally from the Data Processing
Inequality. Mutual information satisfies this new definition of equitability
while MIC does not. Finally, we show that the simulation evidence offered by
Reshef et al. was artifactual. We conclude that estimating mutual information
is not only practical for many real-world applications, but also provides a
natural solution to the problem of quantifying associations in large data sets
Measuring Shared Information and Coordinated Activity in Neuronal Networks
Most nervous systems encode information about stimuli in the responding
activity of large neuronal networks. This activity often manifests itself as
dynamically coordinated sequences of action potentials. Since multiple
electrode recordings are now a standard tool in neuroscience research, it is
important to have a measure of such network-wide behavioral coordination and
information sharing, applicable to multiple neural spike train data. We propose
a new statistic, informational coherence, which measures how much better one
unit can be predicted by knowing the dynamical state of another. We argue
informational coherence is a measure of association and shared information
which is superior to traditional pairwise measures of synchronization and
correlation. To find the dynamical states, we use a recently-introduced
algorithm which reconstructs effective state spaces from stochastic time
series. We then extend the pairwise measure to a multivariate analysis of the
network by estimating the network multi-information. We illustrate our method
by testing it on a detailed model of the transition from gamma to beta rhythms.Comment: 8 pages, 6 figure
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
Brain covariance selection: better individual functional connectivity models using population prior
Spontaneous brain activity, as observed in functional neuroimaging, has been
shown to display reproducible structure that expresses brain architecture and
carries markers of brain pathologies. An important view of modern neuroscience
is that such large-scale structure of coherent activity reflects modularity
properties of brain connectivity graphs. However, to date, there has been no
demonstration that the limited and noisy data available in spontaneous activity
observations could be used to learn full-brain probabilistic models that
generalize to new data. Learning such models entails two main challenges: i)
modeling full brain connectivity is a difficult estimation problem that faces
the curse of dimensionality and ii) variability between subjects, coupled with
the variability of functional signals between experimental runs, makes the use
of multiple datasets challenging. We describe subject-level brain functional
connectivity structure as a multivariate Gaussian process and introduce a new
strategy to estimate it from group data, by imposing a common structure on the
graphical model in the population. We show that individual models learned from
functional Magnetic Resonance Imaging (fMRI) data using this population prior
generalize better to unseen data than models based on alternative
regularization schemes. To our knowledge, this is the first report of a
cross-validated model of spontaneous brain activity. Finally, we use the
estimated graphical model to explore the large-scale characteristics of
functional architecture and show for the first time that known cognitive
networks appear as the integrated communities of functional connectivity graph.Comment: in Advances in Neural Information Processing Systems, Vancouver :
Canada (2010
Estimating sample-specific regulatory networks
Biological systems are driven by intricate interactions among the complex
array of molecules that comprise the cell. Many methods have been developed to
reconstruct network models of those interactions. These methods often draw on
large numbers of samples with measured gene expression profiles to infer
connections between genes (or gene products). The result is an aggregate
network model representing a single estimate for the likelihood of each
interaction, or "edge," in the network. While informative, aggregate models
fail to capture the heterogeneity that is represented in any population. Here
we propose a method to reverse engineer sample-specific networks from aggregate
network models. We demonstrate the accuracy and applicability of our approach
in several data sets, including simulated data, microarray expression data from
synchronized yeast cells, and RNA-seq data collected from human lymphoblastoid
cell lines. We show that these sample-specific networks can be used to study
changes in network topology across time and to characterize shifts in gene
regulation that may not be apparent in expression data. We believe the ability
to generate sample-specific networks will greatly facilitate the application of
network methods to the increasingly large, complex, and heterogeneous
multi-omic data sets that are currently being generated, and ultimately support
the emerging field of precision network medicine
Information decomposition of multichannel EMG to map functional interactions in the distributed motor system
The central nervous system needs to coordinate multiple muscles during postural control. Functional coordination is established through the neural circuitry that interconnects different muscles. Here we used multivariate information decomposition of multichannel EMG acquired from 14 healthy participants during postural tasks to investigate the neural interactions between muscles. A set of information measures were estimated from an instantaneous linear regression model and a time-lagged VAR model fitted to the EMG envelopes of 36 muscles. We used network analysis to quantify the structure of functional interactions between muscles and compared them across experimental conditions. Conditional mutual information and transfer entropy revealed sparse networks dominated by local connections between muscles. We observed significant changes in muscle networks across postural tasks localized to the muscles involved in performing those tasks. Information decomposition revealed distinct patterns in task-related changes: unimanual and bimanual pointing were associated with reduced transfer to the pectoralis major muscles, but an increase in total information compared to no pointing, while postural instability resulted in increased information, information transfer and information storage in the abductor longus muscles compared to normal stability. These findings show robust patterns of directed interactions between muscles that are task-dependent and can be assessed from surface EMG recorded during static postural tasks. We discuss directed muscle networks in terms of the neural circuitry involved in generating muscle activity and suggest that task-related effects may reflect gain modulations of spinal reflex pathways
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