Large-scale directed network inference with multivariate transfer entropy and hierarchical statistical testing

Novelli, Leonardo; Wollstadt, Patricia; Mediano, Pedro A. M.; Wibral, Michael; Lizier, Joseph T.

doi:10.1162/netn_a_00092

Cited by 95 publications

(153 citation statements)

References 71 publications

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“…More specifically, we expect that the tail of the out-degree distribution would be fattened, and the rich-club coefficient [49] may be underestimated. These implications also apply to iterative or greedy algorithms based on multivariate TE [50][51][52][53][54], since they rely on computing the pairwise TE as a first step. TE beyond the effect of the in-degrees.…”

Section: Discussionmentioning

confidence: 99%

Deriving pairwise transfer entropy from network structure and motifs

et al. 2020

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Transfer entropy (TE) is an established method for quantifying directed statistical dependencies in neuroimaging and complex systems datasets. The pairwise (or bivariate) TE from a source to a target node in a network does not depend solely on the local source-target link weight, but on the wider network structure that the link is embedded in. This relationship is studied using a discrete-time linearly coupled Gaussian model, which allows us to derive the TE for each link from the network topology. It is shown analytically that the dependence on the directed link weight is only a first approximation, valid for weak coupling. More generally, the TE increases with the in-degree of the source and decreases with the in-degree of the target, indicating an asymmetry of information transfer between hubs and low-degree nodes. In addition, the TE is directly proportional to weighted motif counts involving common parents or multiple walks from the source to the target, which are more abundant in networks with a high clustering coefficient than in random networks. Our findings also apply to Granger causality, which is equivalent to TE for Gaussian variables. Moreover, similar empirical results on random Boolean networks suggest that the dependence of the TE on the in-degree extends to nonlinear dynamics.

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Section: Discussionmentioning

confidence: 99%

Deriving pairwise transfer entropy from network structure and motifs

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“…Functional connectivity estimated by transfer entropy. In order to quantify compute functional connectivity (the amount of cross-regional interaction) we used transfer entropy (TE) as a directed information-theoretic metric for estimating the relationship between the past activity state of a source region and the present activity state of a target region (27,29,30). In its basic form, the Bivariate TE (BTE) between variables and is defined as the Mutual Information (MI) between the current value of , and the past value of −1 , conditioned on the immediate past values of −1 .…”

Section: Methodsmentioning

confidence: 99%

“…We examined mesoscale functional connectivity on the two relevant timescales: throughout learning and within trials. We estimated functional connectivity using transfer entropy (TE) (27)(28)(29). TE is a directed measure of connectivity, which estimates functional connectivity based on information-theoretic measures of regional activity distributions across trials and time steps.…”

Section: Stimulus-related Functional Connectivity Grows During Learningmentioning

confidence: 99%

Mesoscale brain dynamics reorganizes and stabilizes during learning

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Novelli

et al. 2020

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Adaptive behavior is coordinated by neuronal networks that are distributed across multiple brain regions. How cross-regional interactions reorganize during learning remains elusive. We applied multi-fiber photometry to chronically record simultaneous activity of 12-48 mouse brain regions while mice learned a tactile discrimination task. We found that with learning most regions shifted their peak activity from reward-related action to the reward-predicting stimulus. We corroborated this finding by functional connectivity estimation using transfer entropy, which revealed growth and stabilization of mesoscale networks encompassing basal ganglia, thalamus, cortex, and hippocampus, especially during stimulus presentation. The internal globus pallidus, ventromedial thalamus, and several regions in frontal cortex emerged as hub regions. Our results highlight the cooperative action of distributed brain regions to establish goal-oriented mesoscale network dynamics during learning.

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“…where I(· : ·|·) is the conditional mutual information and Y + , Y − , X − are, respectively, a future random variable of the process Y, a vector of suitably chosen past random variables of the past of that process, and a suitably chosen vector of past random variables of the process X (see [1,[8][9][10][11] for considerations on the correct choice of the past random variables). TE measures the amount of information transferred between a single source and a single target process.…”

Section: Background Technical Background: Transfer Entropy and Multivmentioning

confidence: 99%

“…Computing the mT E tot in equation 2 exactly is an NP-hard problem [14], and approximations are necessary for practical use. This problem was recently addressed in [15,16], with the implementation of an approximate greedy algorithm in the IDT xl toolbox, which allows a large-scale directed network inference with mTE [11] and is freely available from GitHub (https://github.com/pwollstadt/IDTxl). IDTxl performs a greedy algorithm with an iterative sequence of statistical steps to infer the 'relevant' sources of the network, thus reducing the dimensionality of the problem, and allows to properly construct the nonuniform embedding of source and target time-series [17,18], i.e.…”

Section: Background Technical Background: Transfer Entropy and Multivmentioning

confidence: 99%

Measuring spectrally-resolved information transfer for sender- and receiver-specific frequencies

Pinzuti

Wollsdtadt

Gutknecht

et al. 2020

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Information transfer, measured by transfer entropy, is a key component of distributed computation. It is therefore important to understand the pattern of information transfer in order to unravel the distributed computational algorithms of a system. Since in many natural systems distributed computation is thought to rely on rhythmic processes a frequency resolved measure of information transfer is highly desirable. Here, we present a novel algorithm, and its efficient implementation, to identify separately frequencies sending and receiving information in a network. Our approach relies on the invertible maximum overlap discrete wavelet transform (MODWT) for the creation of surrogate data in the computation of transfer entropy and entirely avoids filtering of the original signals. The approach thereby avoids well-known problems due to phase shifts or the ineffectiveness of filtering in the information theoretic setting. We also show that measuring frequency-resolved information transfer is a partial information decomposition problem that cannot be fully resolved to date and discuss the implications of this issue. Last, we evaluate the performance of our algorithm on simulated data and apply it to human magnetoencephalography (MEG) recordings and to local field potential recordings in the ferret. In human MEG we demonstrate top-down information flow in temporal cortex from very high frequencies (above 100Hz) to both similarly high frequencies and to frequencies around 20Hz, i.e. a complex spectral configuration of cortical information transmission that has not been described before. In the ferret we show that the prefrontal cortex sends information at low frequencies (4-8 Hz) to early visual cortex (V1), while V1 receives the information at high frequencies (> 125 Hz). Author SummarySystems in nature that perform computations typically consist of a large number of relatively simple but interacting parts. In human brains, for example, billions of neurons work together to enable our cognitive abilities. This well-orchestrated teamwork requires information to be exchanged very frequently. In many cases this exchange February 8, 2020 1/37 happens rhythmically and, therefore, it seems beneficial for our understanding of physical systems if we could link the information exchange to specific rhythms. We here present a method to determine which rhythms send, and which rhythms receive information. Since many rhythms can interact at both sender and receiver side, we show that the interpretation of results always needs to consider that the above problem is tightly linked to partial information decomposition -an intriguing problem from information theory only solved recently, and only partly. We applied our novel method to information transfer in the human inferior temporal cortex, a brain region relevant for object perception, and unexpectedly found information transfer originating at very high frequencies at 100Hz and then forking to be received at both similarly high but also much lower frequencies around 20Hz. These results ...

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Large-scale directed network inference with multivariate transfer entropy and hierarchical statistical testing

Cited by 95 publications

References 71 publications

Deriving pairwise transfer entropy from network structure and motifs

Deriving pairwise transfer entropy from network structure and motifs

Mesoscale brain dynamics reorganizes and stabilizes during learning

Measuring spectrally-resolved information transfer for sender- and receiver-specific frequencies

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