Large-scale nonlinear Granger causality for inferring directed dependence from short multivariate time-series data

Sex-dependent nonlinear Granger connectivity patterns of brain aging in healthy population

BACKGROUND

Brain aging is a complex process that involves functional alterations in multiple subnetworks and brain regions. However, most previous studies investigating aging-related functional connectivity (FC) changes using resting-state functional magnetic resonance images (rs-fMRIs) have primarily focused on the linear correlation between brain subnetworks, ignoring the nonlinear casual properties of fMRI signals.

METHODS

We introduced the neural Granger causality technique to investigate the sex-dependent nonlinear Granger connectivity (NGC) during aging on a publicly available dataset of 227 healthy participants acquired cross-sectionally in Leipzig, Germany.

RESULTS

Our findings indicate that brain aging may cause widespread declines in NGC at both regional and subnetwork scales. These findings exhibit high reproducibility across different network sparsities, demonstrating the efficacy of static and dynamic analysis strategies. Females exhibit greater heterogeneity and reduced stability in NGC compared to males during aging, especially the NGC between the visual network and other subnetworks. Besides, NGC strengths can well reflect the individual cognitive function, which may therefore work as a sensitive metric in cognition-related experiments for individual-scale or group-scale mechanism understanding.

CONCLUSION

These findings indicate that NGC analysis is a potent tool for identifying sex-dependent brain aging patterns. Our results offer valuable perspectives that could substantially enhance the understanding of sex differences in neurological diseases in the future, especially in degenerative disorders.

Predicting public mental health needs in a crisis using social media indicators: a Singapore big data study

Mental health issues have increased substantially since the onset of the COVID-19 pandemic. However, health policymakers do not have adequate data and tools to predict mental health demand, especially amid a crisis. Using time-series data collected in Singapore, this study examines if and how algorithmically measured emotion indicators from Twitter posts can help forecast emergency mental health needs. We measured the mental health needs during 549 days from 1 July 2020 to 31 December 2021 using the public's daily visits to the emergency room of the country's largest psychiatric hospital and the number of users with "crisis" state assessed through a government-initiated online mental health self-help portal. Pairwise Granger-causality tests covering lag length from 1 day to 5 days indicated that forecast models using Twitter joy, anger and sadness emotions as predictors perform significantly better than baseline models using past mental health needs data alone (e.g., Joy Intensity on IMH Visits, χ2 = 14·9, P < ·001***; Sadness Count on Mindline Crisis, χ2 = 4·6, P = ·031*, with a one-day lag length). The findings highlight the potential of new early indicators for tracking emerging public mental health needs.

Description length guided nonlinear unified Granger causality analysis

Most Granger causality analysis (GCA) methods still remain a two-stage scheme guided by different mathematical theories; both can actually be viewed as the same generalized model selection issues. Adhering to Occam's razor, we present a unified GCA (uGCA) based on the minimum description length principle. In this research, considering the common existence of nonlinearity in functional brain networks, we incorporated the nonlinear modeling procedure into the proposed uGCA method, in which an approximate representation of Taylor's expansion was adopted. Through synthetic data experiments, we revealed that nonlinear uGCA was obviously superior to its linear representation and the conventional GCA. Meanwhile, the nonlinear characteristics of high-order terms and cross-terms would be successively drowned out as noise levels increased. Then, in real fMRI data involving mental arithmetic tasks, we further illustrated that these nonlinear characteristics in fMRI data may indeed be drowned out at a high noise level, and hence a linear causal analysis procedure may be sufficient. Next, involving autism spectrum disorder patients data, compared with conventional GCA, the network property of causal connections obtained by uGCA methods appeared to be more consistent with clinical symptoms.

The arrow-of-time in neuroimaging time series identifies causal triggers of brain function

Moving from association to causal analysis of neuroimaging data is crucial to advance our understanding of brain function. The arrow-of-time (AoT), that is, the known asymmetric nature of the passage of time, is the bedrock of causal structures shaping physical phenomena. However, almost all current time series metrics do not exploit this asymmetry, probably due to the difficulty to account for it in modeling frameworks. Here, we introduce an AoT-sensitive metric that captures the intensity of causal effects in multivariate time series, and apply it to high-resolution functional neuroimaging data. We find that causal effects underlying brain function are more distinctively localized in space and time than functional activity or connectivity, thereby allowing us to trace neural pathways recruited in different conditions. Overall, we provide a mapping of the causal brain that challenges the association paradigm of brain function.

Information theoretic measures of causal influences during transient neural events

Introduction: Transient phenomena play a key role in coordinating brain activity at multiple scales, however their underlying mechanisms remain largely unknown. A key challenge for neural data science is thus to characterize the network interactions at play during these events. Methods: Using the formalism of Structural Causal Models and their graphical representation, we investigate the theoretical and empirical properties of Information Theory based causal strength measures in the context of recurring spontaneous transient events. Results: After showing the limitations of Transfer Entropy and Dynamic Causal Strength in this setting, we introduce a novel measure, relative Dynamic Causal Strength, and provide theoretical and empirical support for its benefits. Discussion: These methods are applied to simulated and experimentally recorded neural time series and provide results in agreement with our current understanding of the underlying brain circuits.

Causality in cardiorespiratory signals in pediatric cardiac patients

Four different Granger causality-based methods - one linear and three nonlinear (Granger Causality, Kernel Granger Causality, large-scale Nonlinear Granger Causality, and Neural Network Granger Causality) were used for assessment and causal-based quantification of the respiratory sinus arrythmia (RSA) in the group of pediatric cardiac patients, based on the single-lead ECG and impedance pneumography signals (the latter as the tidal volume curve equivalent). Each method was able to detect the dependency (in terms of causal inference) between respiratory and cardiac signals. The correlations between quantified RSA and the demographic parameters were also studied, but the results differ for each method. Clinical relevance- The presented methods (among which NNGC seems to be the most valid) allow for quantification of RSA and study of dependency between tidal volume and RR intervals which may help to better understand association between respiratory and cardiovascular systems in different populations.

Causal Inference in Time Series in Terms of Rényi Transfer Entropy

Uncovering causal interdependencies from observational data is one of the great challenges of a nonlinear time series analysis. In this paper, we discuss this topic with the help of an information-theoretic concept known as Rényi’s information measure. In particular, we tackle the directional information flow between bivariate time series in terms of Rényi’s transfer entropy. We show that by choosing Rényi’s parameter α, we can appropriately control information that is transferred only between selected parts of the underlying distributions. This, in turn, is a particularly potent tool for quantifying causal interdependencies in time series, where the knowledge of “black swan” events, such as spikes or sudden jumps, are of key importance. In this connection, we first prove that for Gaussian variables, Granger causality and Rényi transfer entropy are entirely equivalent. Moreover, we also partially extend these results to heavy-tailed α-Gaussian variables. These results allow establishing a connection between autoregressive and Rényi entropy-based information-theoretic approaches to data-driven causal inference. To aid our intuition, we employed the Leonenko et al. entropy estimator and analyzed Rényi’s information flow between bivariate time series generated from two unidirectionally coupled Rössler systems. Notably, we find that Rényi’s transfer entropy not only allows us to detect a threshold of synchronization but it also provides non-trivial insight into the structure of a transient regime that exists between the region of chaotic correlations and synchronization threshold. In addition, from Rényi’s transfer entropy, we could reliably infer the direction of coupling and, hence, causality, only for coupling strengths smaller than the onset value of the transient regime, i.e., when two Rössler systems are coupled but have not yet entered synchronization.

Granger causality test with nonlinear neural-network-based methods: Python package and simulation study

BACKGROUND AND OBJECTIVE

Causality defined by Granger in 1969 is a widely used concept, particularly in neuroscience and economics. As there is an increasing interest in nonlinear causality research, a Python package with a neural-network-based causality analysis approach was created. It allows performing causality tests using neural networks based on Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), or Multilayer Perceptron (MLP). The aim of this paper is to present the nonlinear method for causality analysis and the created Python package.

METHODS

The created functions with the autoregressive (AR) and Generalized Radial Basis Functions (GRBF) neural network models were tested on simulated signals in two cases: with nonlinear dependency and with absence of causality from Y to X signal. The train-test split (70/30) was used. Errors obtained on the test set were compared using the Wilcoxon signed-rank test to determine the presence of the causality. For the chosen model, the proposed method of study the change of causality over time was presented.

RESULTS

In the case when X was a polynomial of Y, nonlinear methods were able to detect the causality, while the AR model did not manage to indicate it. The best results (in terms of the prediction accuracy) were obtained for the MLP for the lag of 150 (MSE equal to 0.011, compared to 0.041 and 0.036 for AR and GRBF, respectively). When there was no causality between the signals, none of the proposed and AR models did indicate false causality, while it was detected by GRBF models in one case. Only the proposed models gave the expected results in each of the tested scenarios.

CONCLUSIONS

The proposed method appeared to be superior to the compared methods. They were able to detect non-linear causality, make accurate forecasting and not indicate false causality. The created package enables easy usage of neural networks to study the causal relationship between signals. The neural-networks-based approach is a suitable method that allows the detection of a nonlinear causal relationship, which cannot be detected by the classical Granger method. Unlike other similar tools, the package allows for the study of changes in causality over time.