Identifying Effective Connectivity between Stochastic Neurons with Variable-Length Memory Using a Transfer Entropy Rate Estimator.

Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X:=Xt:t∈Z and Y:=Yt:t∈Z, which take values in binary alphabets. When the bivariate process (X,Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test-no causal influence-requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons.

Detection of Blood CO2 Influences on Cerebral Hemodynamics Using Transfer Entropy.

Cerebral hemodynamics describes an important physiological system affected by components such as blood pressure, CO2 levels, and endothelial factors. Recently, novel techniques have emerged to analyse cerebral hemodynamics based on the calculation of entropies, which quantifies or describes changes in the complexity of this system when it is affected by a pathological or physiological influence. One recently described measure is transfer entropy, which allows for the determination of causality between the various components of a system in terms of their flow of information, and has shown positive results in the multivariate analysis of physiological signals. This study aims to determine whether conditional transfer entropy reflects the causality in terms of entropy generated by hypocapnia on cerebral hemodynamics. To achieve this, non-invasive signals from 28 healthy individuals who undertook a hyperventilation maneuver were analyzed using conditional transfer entropy to assess the variation in the relevance of CO2 levels on cerebral blood velocity. By employing a specific method to discretize the signals, it was possible to differentiate the influence of CO2 levels during the hyperventilation phase (22.0% and 20.3% increase for the left and right hemispheres, respectively) compared to normal breathing, which remained higher during the recovery phase (15.3% and 15.2% increase, respectively).

Influence of Transfer Entropy in the Short-Term Prediction of Financial Time Series Using an ∊-Machine.

Predicting the values of a financial time series is mainly a function of its price history, which depends on several factors, internal and external. With this history, it is possible to build an ∊-machine for predicting the financial time series. This work proposes considering the influence of a financial series through the transfer of entropy when the values of the other financial series are known. A method is proposed that considers the transfer of entropy for breaking the ties that occur when calculating the prediction with the ∊-machine. This analysis is carried out using data from six financial series: two American, the S&P 500 and the Nasdaq; two Asian, the Hang Seng and the Nikkei 225; and two European, the CAC 40 and the DAX. This work shows that it is possible to influence the prediction of the closing value of a series if the value of the influencing series is known. This work showed that the series that transfer the most information through entropy transfer are the American S&P 500 and Nasdaq, followed by the European DAX and CAC 40, and finally the Asian Nikkei 225 and Hang Seng.

Twitter Sentiment Analysis and Influence on Stock Performance Using Transfer Entropy and EGARCH Methods.

Financial economic research has extensively documented the fact that the impact of the arrival of negative news on stock prices is more intense than that of the arrival of positive news. The authors of the present study followed an innovative approach based on the utilization of two artificial intelligence algorithms to test that asymmetric response effect. Methods: The first algorithm was used to web-scrape the social network Twitter to download the top tweets of the 24 largest market-capitalized publicly traded companies in the world during the last decade. A second algorithm was then used to analyze the contents of the tweets, converting that information into social sentiment indexes and building a time series for each considered company. After comparing the social sentiment indexes' movements with the daily closing stock price of individual companies using transfer entropy, our estimations confirmed that the intensity of the impact of negative and positive news on the daily stock prices is statistically different, as well as that the intensity with which negative news affects stock prices is greater than that of positive news. The results support the idea of the asymmetric effect that negative sentiment has a greater effect than positive sentiment, and these results were confirmed with the EGARCH model.

What Drives Bitcoin? An Approach from Continuous Local Transfer Entropy and Deep Learning Classification Models.

Bitcoin has attracted attention from different market participants due to unpredictable price patterns. Sometimes, the price has exhibited big jumps. Bitcoin prices have also had extreme, unexpected crashes. We test the predictive power of a wide range of determinants on bitcoins' price direction under the continuous transfer entropy approach as a feature selection criterion. Accordingly, the statistically significant assets in the sense of permutation test on the nearest neighbour estimation of local transfer entropy are used as features or explanatory variables in a deep learning classification model to predict the price direction of bitcoin. The proposed variable selection do not find significative the explanatory power of NASDAQ and Tesla. Under different scenarios and metrics, the best results are obtained using the significant drivers during the pandemic as validation. In the test, the accuracy increased in the post-pandemic scenario of July 2020 to January 2021 without drivers. In other words, our results indicate that in times of high volatility, Bitcoin seems to self-regulate and does not need additional drivers to improve the accuracy of the price direction.

Network Analysis of Multivariate Transfer Entropy of Cryptocurrencies in Times of Turbulence.

We investigate the effects of the recent financial turbulence of 2020 on the market of cryptocurrencies taking into account the hourly price and volume of transactions from December 2019 to April 2020. The data were subdivided into time frames and analyzed the directed network generated by the estimation of the multivariate transfer entropy. The approach followed here is based on a greedy algorithm and multiple hypothesis testing. Then, we explored the clustering coefficient and the degree distributions of nodes for each subperiod. It is found the clustering coefficient increases dramatically in March and coincides with the most severe fall of the recent worldwide stock markets crash. Further, the log-likelihood in all cases bent over a power law distribution, with a higher estimated power during the period of major financial contraction. Our results suggest the financial turbulence induce a higher flow of information on the cryptocurrency market in the sense of a higher clustering coefficient and complexity of the network. Hence, the complex properties of the multivariate transfer entropy network may provide early warning signals of increasing systematic risk in turbulence times of the cryptocurrency markets.

Optimal Interplay between Synaptic Strengths and Network Structure Enhances Activity Fluctuations and Information Propagation in Hierarchical Modular Networks.

In network models of spiking neurons, the joint impact of network structure and synaptic parameters on activity propagation is still an open problem. Here, we use an information-theoretical approach to investigate activity propagation in spiking networks with a hierarchical modular topology. We observe that optimized pairwise information propagation emerges due to the increase of either (i) the global synaptic strength parameter or (ii) the number of modules in the network, while the network size remains constant. At the population level, information propagation of activity among adjacent modules is enhanced as the number of modules increases until a maximum value is reached and then decreases, showing that there is an optimal interplay between synaptic strength and modularity for population information flow. This is in contrast to information propagation evaluated among pairs of neurons, which attains maximum value at the maximum values of these two parameter ranges. By examining the network behavior under the increase of synaptic strength and the number of modules, we find that these increases are associated with two different effects: (i) the increase of autocorrelations among individual neurons and (ii) the increase of cross-correlations among pairs of neurons. The second effect is associated with better information propagation in the network. Our results suggest roles that link topological features and synaptic strength levels to the transmission of information in cortical networks.

A Data-Driven Measure of Effective Connectivity Based on Renyi's α-Entropy.

Transfer entropy (TE) is a model-free effective connectivity measure based on information theory. It has been increasingly used in neuroscience because of its ability to detect unknown non-linear interactions, which makes it well suited for exploratory brain effective connectivity analyses. Like all information theoretic quantities, TE is defined regarding the probability distributions of the system under study, which in practice are unknown and must be estimated from data. Commonly used methods for TE estimation rely on a local approximation of the probability distributions from nearest neighbor distances, or on symbolization schemes that then allow the probabilities to be estimated from the symbols' relative frequencies. However, probability estimation is a challenging problem, and avoiding this intermediate step in TE computation is desirable. In this work, we propose a novel TE estimator using functionals defined on positive definite and infinitely divisible kernels matrices that approximate Renyi's entropy measures of order α. Our data-driven approach estimates TE directly from data, sidestepping the need for probability distribution estimation. Also, the proposed estimator encompasses the well-known definition of TE as a sum of Shannon entropies in the limiting case when α → 1. We tested our proposal on a simulation framework consisting of two linear models, based on autoregressive approaches and a linear coupling function, respectively, and on the public electroencephalogram (EEG) database BCI Competition IV, obtained under a motor imagery paradigm. For the synthetic data, the proposed kernel-based TE estimation method satisfactorily identifies the causal interactions present in the data. Also, it displays robustness to varying noise levels and data sizes, and to the presence of multiple interaction delays in the same connected network. Obtained results for the motor imagery task show that our approach codes discriminant spatiotemporal patterns for the left and right-hand motor imagination tasks, with classification performances that compare favorably to the state-of-the-art.

Disruption of transfer entropy and inter-hemispheric brain functional connectivity in patients with disorder of consciousness.

Severe traumatic brain injury can lead to disorders of consciousness (DOC) characterized by deficit in conscious awareness and cognitive impairment including coma, vegetative state, minimally consciousness, and lock-in syndrome. Of crucial importance is to find objective markers that can account for the large-scale disturbances of brain function to help the diagnosis and prognosis of DOC patients and eventually the prediction of the coma outcome. Following recent studies suggesting that the functional organization of brain networks can be altered in comatose patients, this work analyzes brain functional connectivity (FC) networks obtained from resting-state functional magnetic resonance imaging (rs-fMRI). Two approaches are used to estimate the FC: the Partial Correlation (PC) and the Transfer Entropy (TE). Both the PC and the TE show significant statistical differences between the group of patients and control subjects; in brief, the inter-hemispheric PC and the intra-hemispheric TE account for such differences. Overall, these results suggest two possible rs-fMRI markers useful to design new strategies for the management and neuropsychological rehabilitation of DOC patients.