Network Inference and Maximum Entropy Estimation on Information Diagrams

Martin, Elliot A.; Hlinka, Jaroslav; Meinke, Alexander; Děchtěrenko, Filip; Tintěra, Jaroslav; Oliver, Isaura; Davidsen, Jörn

doi:10.1038/s41598-017-06208-w

Cited by 10 publications

(9 citation statements)

References 49 publications

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“…This suggests that only when accounting also for non-linear coupling, the bivariate dependencies provide sufficient data structure approximation resolving the apparent inconsistency of the results in [19]. This is also true for other brain networks [37].…”

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confidence: 79%

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Pairwise network information and nonlinear correlations

2016

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Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the units can be considered pairwise and, thus, can be modeled as an interaction network with simple links corresponding to pairwise interactions. In principle this can be determined by comparing the maximum entropy given the bivariate probability distributions to the true joint entropy. In many practical cases this is not an option since the bivariate distributions needed may not be reliably estimated, or the optimization is too computationally expensive. Here we present an approach that allows one to use mutual informations as a proxy for the bivariate probability distributions. This has the advantage of being less computationally expensive and easier to estimate. We achieve this by introducing a novel entropy maximization scheme that is based on conditioning on entropies and mutual informations. This renders our approach typically superior to other methods based on linear approximations. The advantages of the proposed method are documented using oscillator networks and a resting-state human brain network as generic relevant examples. Pairwise measures of dependence such as crosscorrelations (as measured by the Pearson correlation coefficient or covariance matrix) and mutual information are widely used to characterize the interactions within complex systems. They are a key ingredient to techniques such as principal component analysis, empirical orthogonal functions, and functional networks (networks inferred from dynamical time series) [1][2][3]. These techniques are widespread since they provide greatly simplified descriptions of complex systems, and allow for the analysis of what might otherwise be intractable problems [4]. In particular, functional networks have been widely applied in fields such as neuroscience [4,5], genetics [6], and cell physiology [7], as well as in climate research [1,8].In this paper we study how faithfully these measures alone can represent a given system. With the increasing use of functional networks this topic has received much attention recently, and many technical concerns have been brought to light dealing with the inference of these networks. Previous studies have shown that the estimates of the functional networks can be negatively affected by properties of the time series [9][10][11], as well as properties of the measure of association, e.g. crosscorrelations [12][13][14][15]. In this work however, we address a more fundamental question: How well do pairwise measurements represent a system?In principle this can be evaluated using a maximum entropy approach. The corresponding framework was first laid out in [16] and later applied in [17], where they assessed the rationale of only looking at the pairwise correlations between neurons. They examined how well the maximum entropy distribution, consistent with all the pairwise correlations described...

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confidence: 79%

“…Alternatively, estimators for continuous variables can be used as we discuss in [37]. To provide clear proofs of principle, we first focus on three-oscillator systems in the following as this is the smallest system size at which the results are non-trivial.…”

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confidence: 99%

Pairwise network information and nonlinear correlations

2016

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“…4 for partial correlation matrices). To limit the number of spurious connections from the estimating process of partial correlation (Martin et al, 2017; Oliver et al, 2019), all partial correlations were tested for statistical significance (Epskamp and Fried, 2018). Then the strongest 80% of connections in each network were preserved to equalizes the network sizes.…”

Section: Resultsmentioning

confidence: 99%

Prenatal Stress Dysregulates Resting-State Functional Connectivity and Sensory Motifs

Jafari

Rezaei

Afrashteh

et al. 2020

Preprint

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Prenatal stress (PS) can impact fetal brain structure and function and lead to higher vulnerability to neurodevelopmental and neuropsychiatric disorders. To understand how PS alters evoked and spontaneous cortical activity and intrinsic brain functional connectivity, mesoscale voltage imaging was performed in adult C57BL/6NJ mice who were exposed to an auditory stress paradigm on gestational days 12-16. PS mice demonstrated a four-fold higher basal corticosterone level, reduced amplitude of all cortical sensory-evoked responses (visual, auditory, whisker, forelimb, and hindlimb), decreased overall resting-state functional connectivity, declined network efficiency, reduced inter-module connectivity, enhanced intra-module connectivity, and altered frequency of auditory and forelimb spontaneous sensory motifs relative to control animals. In fact, for PS, the resting-state functional connectivity changes drastically towards an overall less connected structure that consists of largely disjoint but tight modules, leading to a declined network efficiency. The changes in structure also indicate that the posterior secondary motor, primary barrel, and secondary hindlimb cortices are cortical areas with higher susceptibility to dysfunction. Our findings highlight the PS modulation of brain functional connectivity that can pose offspring at risk for stress-related neuropsychiatric disorders.

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“…These include but are not limited to methods based on the maximum entropy principle, cf. [21], and time series graphs, cf. [22], as well as methods based on delay-coordinate embedding (the Takens embedding theorem [23]) to reconstruct the nonlinear dynamics [24][25][26][27][28].…”

Section: Prediction and Causalitymentioning

confidence: 99%

Challenges in the analysis of complex systems: introduction and overview

Hastings

Davidsen

Leung

2017

Eur. Phys. J. Spec. Top.

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One of the main challenges of modern physics is to provide a systematic understanding of systems far from equilibrium exhibiting emergent behavior. Prominent examples of such complex systems include, but are not limited to the cardiac electrical system, the brain, the power grid, social systems, material failure and earthquakes, and the climate system. Due to the technological advances over the last decade, the amount of observations and data available to characterize complex systems and their dynamics, as well as the capability to process that data, has increased substantially. The present issue discusses a cross section of the current research on complex systems, with a focus on novel experimental and data-driven approaches to complex systems that provide the necessary platform to model the behavior of such systems.

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Network Inference and Maximum Entropy Estimation on Information Diagrams

Cited by 10 publications

References 49 publications

Pairwise network information and nonlinear correlations

Pairwise network information and nonlinear correlations

Prenatal Stress Dysregulates Resting-State Functional Connectivity and Sensory Motifs

Challenges in the analysis of complex systems: introduction and overview

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