Measuring information-transfer delays

In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener’s principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics

Causal Discovery from Temporal Data: An Overview and New Perspectives

Temporal data, representing chronological observations of complex systems, has always been a typical data structure that can be widely generated by many domains, such as industry, medicine and finance. Analyzing this type of data is extremely valuable for various applications. Thus, different temporal data analysis tasks, eg, classification, clustering and prediction, have been proposed in the past decades. Among them, causal discovery, learning the causal relations from temporal data, is considered an interesting yet critical task and has attracted much research attention. Existing casual discovery works can be divided into two highly correlated categories according to whether the temporal data is calibrated, ie, multivariate time series casual discovery, and event sequence casual discovery. However, most previous surveys are only focused on the time series casual discovery and ignore the second category. In this paper, we specify the correlation between the two categories and provide a systematical overview of existing solutions. Furthermore, we provide public datasets, evaluation metrics and new perspectives for temporal data casual discovery.Comment: 52 pages, 6 figure

Estimating causal networks in biosphere–atmosphere interaction with the PCMCI approach

Local meteorological conditions and biospheric activity are tightly coupled. Understanding these links is an essential prerequisite for predicting the Earth system under climate change conditions. However, many empirical studies on the interaction between the biosphere and the atmosphere are based on correlative approaches that are not able to deduce causal paths, and only very few studies apply causal discovery methods. Here, we use a recently proposed causal graph discovery algorithm, which aims to reconstruct the causal dependency structure underlying a set of time series. We explore the potential of this method to infer temporal dependencies in biosphere-atmosphere interactions. Specifically we address the following questions: How do periodicity and heteroscedasticity influence causal detection rates, i.e. the detection of existing and non-existing links? How consistent are results for noise-contaminated data? Do results exhibit an increased information content that justifies the use of this causal-inference method? We explore the first question using artificial time series with well known dependencies that mimic real-world biosphere-atmosphere interactions. The two remaining questions are addressed jointly in two case studies utilizing observational data. Firstly, we analyse three replicated eddy covariance datasets from a Mediterranean ecosystem at half hourly time resolution allowing us to understand the impact of measurement uncertainties. Secondly, we analyse global NDVI time series (GIMMS 3g) along with gridded climate data to study large-scale climatic drivers of vegetation greenness. Overall, the results confirm the capacity of the causal discovery method to extract time-lagged linear dependencies under realistic settings. The violation of the method's assumptions increases the likelihood to detect false links. Nevertheless, we consistently identify interaction patterns in observational data. Our findings suggest that estimating a directed biosphere-atmosphere network at the ecosystem level can offer novel possibilities to unravel complex multi-directional interactions. Other than classical correlative approaches, our findings are constrained to a few meaningful set of relations which can be powerful insights for the evaluation of terrestrial ecosystem models

Causal influence of brainstem response to transcutaneous vagus nerve stimulation on cardiovagal outflow

background: the autonomic response to transcutaneous auricular vagus nerve stimulation (taVNS) has been linked to the engagement of brainstem circuitry modulating autonomic outflow. However, the physiological mechanisms supporting such efferent vagal responses are not well understood, particularly in humans. hypothesis: we present a paradigm for estimating directional brain-heart interactions in response to taVNS. We propose that our approach is able to identify causal links between the activity of brainstem nuclei involved in autonomic control and cardiovagal outflow. methods: we adopt an approach based on a recent reformulation of granger causality that includes permutation-based, nonparametric statistics. The method is applied to ultrahigh field (7T) functional magnetic resonance imaging (fMRI) data collected on healthy subjects during taVNS. results: our framework identified taVNS-evoked functional brainstem responses with superior sensitivity compared to prior conventional approaches, confirming causal links between taVNS stimulation and fMRI response in the nucleus tractus solitarii (NTS). furthermore, our causal approach elucidated potential mechanisms by which information is relayed between brainstem nuclei and cardiovagal, i.e., high-frequency heart rate variability, in response to taVNS. Our findings revealed that key brainstem nuclei, known from animal models to be involved in cardiovascular control, exert a causal influence on taVNS-induced cardiovagal outflow in humans. conclusion: our causal approach allowed us to noninvasively evaluate directional interactions between fMRI BOLD signals from brainstem nuclei and cardiovagal outflow

Functional neural circuits that underlie developmental stuttering

The aim of this study was to identify differences in functional and effective brain connectivity between persons who stutter (PWS) and typically developing (TD) fluent speakers, and to assess whether those differences can serve as biomarkers to distinguish PWS from TD controls. We acquired resting-state functional magnetic resonance imaging data in 44 PWS and 50 TD controls. We then used Independent Component Analysis (ICA) together with Hierarchical Partner Matching (HPM) to identify networks of robust, functionally connected brain regions that were highly reproducible across participants, and we assessed whether connectivity differed significantly across diagnostic groups. We then used Granger Causality (GC) to study the causal interactions (effective connectivity) between the regions that ICA and HPM identified. Finally, we used a kernel support vector machine to assess how well these measures of functional connectivity and granger causality discriminate PWS from TD controls. Functional connectivity was stronger in PWS compared with TD controls in the supplementary motor area (SMA) and primary motor cortices, but weaker in inferior frontal cortex (IFG, Broca’s area), caudate, putamen, and thalamus. Additionally, causal influences were significantly weaker in PWS from the IFG to SMA, and from the basal ganglia to IFG through the thalamus, compared to TD controls. ICA and GC indices together yielded an accuracy of 92.7% in classifying PWS from TD controls. Our findings suggest the presence of dysfunctional circuits that support speech planning and timing cues for the initiation and execution of motor sequences in PWS. Our high accuracy of classification further suggests that these aberrant brain features may serve as robust biomarkers for PWS

A temporal precedence based clustering method for gene expression microarray data

Background: Time-course microarray experiments can produce useful data which can help in understanding the underlying dynamics of the system. Clustering is an important stage in microarray data analysis where the data is grouped together according to certain characteristics. The majority of clustering techniques are based on distance or visual similarity measures which may not be suitable for clustering of temporal microarray data where the sequential nature of time is important. We present a Granger causality based technique to cluster temporal microarray gene expression data, which measures the interdependence between two time-series by statistically testing if one time-series can be used for forecasting the other time-series or not. Results: A gene-association matrix is constructed by testing temporal relationships between pairs of genes using the Granger causality test. The association matrix is further analyzed using a graph-theoretic technique to detect highly connected components representing interesting biological modules. We test our approach on synthesized datasets and real biological datasets obtained for Arabidopsis thaliana. We show the effectiveness of our approach by analyzing the results using the existing biological literature. We also report interesting structural properties of the association network commonly desired in any biological system. Conclusions: Our experiments on synthesized and real microarray datasets show that our approach produces encouraging results. The method is simple in implementation and is statistically traceable at each step. The method can produce sets of functionally related genes which can be further used for reverse-engineering of gene circuits

Modeling gene expression regulatory networks with the sparse vector autoregressive model

<p>Abstract</p> <p>Background</p> <p>To understand the molecular mechanisms underlying important biological processes, a detailed description of the gene products networks involved is required. In order to define and understand such molecular networks, some statistical methods are proposed in the literature to estimate gene regulatory networks from time-series microarray data. However, several problems still need to be overcome. Firstly, information flow need to be inferred, in addition to the correlation between genes. Secondly, we usually try to identify large networks from a large number of genes (parameters) originating from a smaller number of microarray experiments (samples). Due to this situation, which is rather frequent in Bioinformatics, it is difficult to perform statistical tests using methods that model large gene-gene networks. In addition, most of the models are based on dimension reduction using clustering techniques, therefore, the resulting network is not a gene-gene network but a module-module network. Here, we present the Sparse Vector Autoregressive model as a solution to these problems.</p> <p>Results</p> <p>We have applied the Sparse Vector Autoregressive model to estimate gene regulatory networks based on gene expression profiles obtained from time-series microarray experiments. Through extensive simulations, by applying the SVAR method to artificial regulatory networks, we show that SVAR can infer true positive edges even under conditions in which the number of samples is smaller than the number of genes. Moreover, it is possible to control for false positives, a significant advantage when compared to other methods described in the literature, which are based on ranks or score functions. By applying SVAR to actual HeLa cell cycle gene expression data, we were able to identify well known transcription factor targets.</p> <p>Conclusion</p> <p>The proposed SVAR method is able to model gene regulatory networks in frequent situations in which the number of samples is lower than the number of genes, making it possible to naturally infer partial Granger causalities without any <it>a priori </it>information. In addition, we present a statistical test to control the false discovery rate, which was not previously possible using other gene regulatory network models.</p