Conditional Transfer Entropy Research Articles

A temporal information transfer network approach considering federal funds rate for an interpretable asset fluctuation prediction framework

This study explores the complex interdependencies among five major financial assets—S&P 500, Bitcoin, Crude Oil, Gold, and USD/EUR—from April 2015 to September 2022, emphasizing the importance of understanding global financial dynamics for robust financial management. We quantitatively analyze daily causal relationships using conditional transfer entropy, a method that surpasses traditional correlation analyses. By incorporating the effective federal funds rate into our models, we enhance predictive accuracy and account for monetary policy impacts, ensuring our findings are relevant to current economic conditions. Our results reveal significant causal networks, providing key insights into asset interdependencies that support advanced hedging strategies and effective diversification. This research improves prediction models through the innovative use of network-based features and offers practical strategies for managing multinational financial assets, with relevance across various economic scenarios.

Inferring Dealer Networks in the Foreign Exchange Market Using Conditional Transfer Entropy: Analysis of a Central Bank Announcement.

The foreign exchange (FX) market has evolved into a complex system where locally generated information percolates through the dealer network via high-frequency interactions. Information related to major events, such as economic announcements, spreads rapidly through this network, potentially inducing volatility, liquidity disruptions, and contagion effects across financial markets. Yet, research on the mechanics of information flows in the FX market is limited. In this paper, we introduce a novel approach employing conditional transfer entropy to construct networks of information flows. Leveraging a unique, high-resolution dataset of bid and ask prices, we investigate the impact of an announcement by the European Central Bank on the information transfer within the market. During the announcement, we identify key dealers as information sources, conduits, and sinks, and, through comparison to a baseline, uncover shifts in the network topology.

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).

Causality analysis of large-scale structures in the flow around a wall-mounted square cylinder

The aim of this work is to analyse the formation mechanisms of large-scale coherent structures in the flow around a wall-mounted square cylinder, due to their impact on pollutant transport within cities. To this end, we assess causal relations between the modes of a reduced-order model obtained by applying proper orthogonal decomposition to high-fidelity simulation data of the flow case under study. The causal relations are identified using conditional transfer entropy, which is an information-theoretical quantity that estimates the amount of information contained in the past of one variable about another. This allows for an understanding of the origins and evolution of different phenomena in the flow, with the aim of identifying the modes responsible for the formation of the main vortical structures. Our approach unveils that vortex-breaker modes are the most causal modes, in particular, over higher-order modes, and no significant causal relationships were found for vortex-generator modes. We validate this technique by determining the causal relations present in the nine-equation model of near-wall turbulence developed by Moehliset al.(New J. Phys., vol. 6, 2004, p. 56), which are in good agreement with literature results for turbulent channel flows.

Evaluation of cardiovascular and cerebrovascular control mechanisms in postural orthostatic tachycardia syndrome via conditional transfer entropy: the impact of the respiratory signal type

Objective. Closed loop cardiovascular (CV) and cerebrovascular (CBV) variability interactions are assessed via transfer entropy (TE) from systolic arterial pressure (SAP) to heart period (HP) and vice versa and from mean arterial pressure (MAP) to mean cerebral blood velocity (MCBv) and vice versa. This analysis is exploited to assess the efficiency of baroreflex and cerebral autoregulation. This study aims at characterizing CV and CBV controls in postural orthostatic tachycardiac syndrome (POTS) subjects experiencing exaggerated sympathetic response during orthostatic challenge via unconditional TE and TE conditioned on respiratory activity (R). Approach. In 18 healthy controls (age: 28 ± 13 yrs; 5 males, 13 females) and 15 POTS individuals (age: 29 ± 11 yrs; 3 males, 12 females) we acquired beat-to-beat variability of HP, SAP, MAP and MCBv and two R signals, namely respiratory chest movement (RCM) and capnogram (CAP). Recordings were made at sitting rest and during active standing (STAND). TE was computed via vector autoregressive approach. Main results. We found that: (i) when assessing CV interactions, the increase of the TE from SAP to HP during STAND, indicating baroreflex activation, is detected solely when conditioning on RCM; (ii) when assessing CBV interactions, the impact of R on the TE computation is negligible; (iii) POTS shows baroreflex impairment during STAND; (iv) POTS exhibits a normal CBV response to STAND. Significance. TE is useful for detecting the impairment of specific regulatory mechanisms in POTS. Moreover, using different R signals highlights the sensitivity of CV and CBV controls to specific R aspects.

ANALYSIS OF CARDIOVASCULAR, CARDIORESPIRATORY, AND VASCULO-RESPIRATORY SIGNALS USING DIFFERENT MACHINE LEARNING TECHNIQUES

Many physiological signals such as heart rate (HR), blood pressure (BP), and respiration (RESP) affect each other, and the inter-relation within and between these signals can be linear or nonlinear. Therefore, this paper’s main aim is to extract the relevant features using the information domain coupling technique based on conditional transfer entropy to detect the nonlinearity and coupling changes between the physiological signals and to classify the database using various machine learning classifiers to study the aging changes in the contribution of HR, BP, and RESP. In the proposed work, the physiological signals, i.e. HR, BP, and RESP, were pre-processed using various filtering methods, then features of physiological signals were extracted using linear and nonlinear techniques. After the pre-processing and extraction of features, the extracted features are classified using machine learning classifiers to classify the physiological signal database to study the aging changes in the contribution of HR, BP, and RESP. The data has been taken from the standard Fantasia database of healthy young and old subjects and self-recorded data of healthy young and old subjects for this study. Naive Bayes (NB), Support vector machine (SVM), K-Nearest Neighbor (KNN), Logistic Regression (LR), and Artificial Neural Network (ANN) were trained using five-fold cross-validation on the physiological dataset. It is concluded from the results that by adding the coupling features, the efficiency of the final prediction of the classifier increased from [Formula: see text]% to [Formula: see text]% obtained by LR, [Formula: see text]% to [Formula: see text]% obtained by SVM, [Formula: see text]% to [Formula: see text]% obtained by KNN, [Formula: see text]% to [Formula: see text]% obtained by NB, and [Formula: see text]% to [Formula: see text]% obtained by ANN. The ANN performs well when provided with the coupling features, gives a maximum accuracy of [Formula: see text]% and very high sensitivity of [Formula: see text]% and specificity of [Formula: see text]%, and takes much less computational time, when compared to other machine learning algorithms on same length of database.

Causality detection with matrix-based transfer entropy

Transfer entropy (TE) is a powerful tool for analyzing causality between time series and complex systems. However, it faces two key challenges. First, TE is often used to quantify the pairwise causal direction; yet, in real-world applications, one is always interested in identifying more complex causal relationships, such as indirect causation, common causation, and synergistic effect. Second, the estimation of TE usually relies on probability estimation, which is particularly complicated, or even infeasible for high-dimensional data. In this work, we take TE one step further and develop a pair of measures, the matrix-based conditional transfer entropy (CTEM) and the matrix-based high-order transfer entropy (HTEM). The former can detect both indirect and common causation, while the latter can detect synergistic effect. Making use of the recently proposed matrix-based Rényi’s α-order entropy functional, CTEM and HTEM are defined on the eigenspectrum of a normalized Hermitian matrix of the projected data in kernel space, which avoids the necessity of density estimation and the curse of dimensionality. Experiments on both synthetic and real-world datasets demonstrate the effectiveness of our measures in high-dimensional space, and their superiority in recovering complex causal structures for more than two time series.

A control chart-based symbolic conditional transfer entropy method for root cause analysis of process disturbances

Root cause analysis is an important step in process monitoring. In the related research field, the popular causality analysis technique, transfer entropy (TE), has been adopted for its capability to handle process nonlinearity. Its improved version, conditional TE (CTE), is better suited to multivariate cases, because of its capability of neglecting indirect causal relations. Nevertheless, the conventional CTE is often sensitive to noise, which hampers its performance. This problem can be solved by using the concept of symbolization. Statistical process control (SPC) is an industry-standard methodology for determining process performance. Therefore, it is reasonable to symbolize process measurements based on the SPC information. In this work, a control chart-based symbolic CTE method is proposed, which conducts CTE to analyze the symbolized process data and reveal the causality among variables. Then, the identified causality information is visualized on a causal map. The method performance is quantified with several indices.

Conditional recurrence plots for the investigation of sawteeth pacing with RF modulation

In many areas of research, from neurobiology to nuclear fusion, which investigate complex dynamical systems involving numerous, different and interconnected physical quantities, the application of advanced analysis tools based on Chaos theory and Information theory has provided significant improvements both by supporting theoretical models and by highlighting hidden relationships between quantities characterizing the observed phenomena. The present article is therefore devoted to the analysis of synchronization experiments in magnetically controlled plasmas at JET, involving a ‘target’ quantity (sawteeth) and a ‘driver’ (modulated injected radio frequency) one. The typical approach to such analysis would start from assuming that the coupling between driver and target is free from external influences. However, since sawteeth can occur naturally and constitute a confounding factor in the analysis, by relaxing such an assumption a more realistic description of the system can emerge. The use of the conditional joint recurrence plots, complemented by the conditional transfer entropy, has provided further evidences supporting the effective influence of the pacing on the fast ions populations of both the minority and of the main plasma species in H-mode plasmas. The results highlight specific physical factors affecting the efficiency of the pacing and are in agreement with modelling estimates. The analysis performed then paves the way for future studies on more recent DT pulses performed at JET, and on data from other synchronization experiments.

Satellite Telemetry Data Anomaly Detection Using Causal Network and Feature-Attention-Based LSTM

Most of the data-driven satellite telemetry data anomaly detection methods suffer from high false positive rate (FPR) and poor interpretability. To solve the above problems, we propose an anomaly detection framework using causal network and feature-attention-based long short-term memory (CN-FA-LSTM). In our method, a causal network of telemetry parameters is constructed by calculating normalized modified conditional transfer entropy (NMCTE) and optimized by conditional independence tests based on the conditional mutual information (CMI). Then, a CN-FA-LSTM is established to predict telemetry data, and a nonparametric dynamic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -sigma threshold updating method is proposed to set thresholds. A case study on a real satellite demonstrates that anomaly detection using the CN-FA-LSTM and nonparametric dynamic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -sigma threshold updating has an average F1-score of 0.9462 and an FPR of 0.0021, which are better than the baseline methods. Furthermore, CN-FA-LSTM has a stronger interpretability than other commonly used prediction models. Supplementary experiment on two public datasets verifies the universal applicability of our method.

Blind Wireless Network Topology Inference

This work proposes a framework to discover the topology of a non-collaborative packet-based wireless network using radio-frequency (RF) sensors. The methodology developed is blind, allowing topology sensing of a network whose key features (i.e., number of nodes, physical layer signals, and medium access control (MAC) and routing protocols) are unknown. Because of the wireless medium, over-the-air signals captured by the sensors are mixed; therefore, blind source separation (BSS) and measurement association are used to separate traffic patterns. Then, to infer the topology, we detect directed data flows among nodes by identifying causal relationships between the separated transmitted patterns. We propose causal inference methods such as Granger causality (GC), transfer entropy (TE), and conditional transfer entropy (CTE) that use the times series of traffic profiles, and a solution based on a neural network (NN) that exploits distilled time-based features. The framework is validated on an ad-hoc wireless network accounting for MAC protocol, packet collisions, nodes mobility, the spatial density of sensors, and channel impairments, such as path-loss, shadowing, and noise. Numerical results reveal that the proposed approach reaches a high probability of link detection and a moderate false alarm rate in mild shadowing regimes and low to moderate network nodes mobility.

Quantifying interactions among car drivers using information theory.

Information-theoretic quantities have found wide applications in understanding interactions in complex systems primarily due to their non-parametric nature and ability to capture non-linear relationships. Increasingly popular among these tools is conditional transfer entropy, also known as causation entropy. In the present work, we leverage this tool to study the interaction among car drivers for the first time. Specifically, we investigate whether a driver responds to its immediate front and its immediate rear car to the same extent and whether we can separately quantify these responses. Using empirical data, we learn about the important features related to human driving behavior. Results demonstrate the evidence that drivers respond to both front and rear cars, and the response to their immediate front car increases in the presence of jammed traffic. Our approach provides a data-driven perspective to study interactions and is expected to aid in analyzing traffic dynamics.

Estimating Conditional Transfer Entropy in Time Series Using Mutual Information and Nonlinear Prediction.

We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of new information and improvement of the prediction accuracy provided by the variables. Then, using a greedy approach, the most informative subsets are selected in an iterative way. The algorithm terminates, when the highest ranked variable is not able to significantly improve the accuracy of the prediction as compared to that obtained using the existing selected subsets. In a simulation study, we compare our estimator to existing state-of-the-art methods at different data lengths and directed dependencies strengths. It is demonstrated that the proposed estimator has a significantly higher accuracy than that of existing methods, especially for the difficult case, where the data are highly correlated and coupled. Moreover, we show its false detection of directed dependencies due to instantaneous couplings effect is lower than that of existing measures. We also show applicability of the proposed estimator on real intracranial electroencephalography data.

A Refinement of Recurrence Analysis to Determine the Time Delay of Causality in Presence of External Perturbations.

This article describes a refinement of recurrence analysis to determine the delay in the causal influence between a driver and a target, in the presence of additional perturbations affecting the time series of the response observable. The methodology is based on the definition of a new type of recurrence plots, the Conditional Joint Recurrence plot. The potential of the proposed approach resides in the great flexibility of recurrence plots themselves, which allows extending the technique to more than three quantities. Autoregressive time series, both linear and nonlinear, with different couplings and percentage of additive Gaussian noise have been investigated in detail, with and without outliers. The approach has also been applied to the case of synthetic periodic signals, representing realistic situations of synchronization experiments in thermonuclear fusion. The results obtained have been very positive; the proposed Conditional Joint Recurrence plots have always managed to identify the right interval of the causal influences and are very competitive with alternative techniques such as the Conditional Transfer Entropy.

Cerebrovascular and cardiovascular variability interactions investigated through conditional joint transfer entropy in subjects prone to postural syncope

Objective: A model-based conditional transfer entropy approach was exploited to quantify the information transfer in cerebrovascular (CBV) and cardiovascular (CV) systems in subjects prone to develop postural syncope. Approach: Spontaneous beat-to-beat variations of mean cerebral blood flow velocity (MCBFV) derived from a transcranial Doppler device, heart period (HP) derived from surface electrocardiogram, mean arterial pressure (MAP) and systolic arterial pressure (SAP) derived from finger plethysmographic arterial pressure device were monitored at rest in supine position (REST) and during 60° head-up tilt (TILT) in 13 individuals (age mean ± standard deviation: 28 ± 9 years, min–max range: 18–44 years, 5 males) with a history of recurrent episodes of syncope (SYNC) and in 13 age- and gender-matched controls (NonSYNC). Respiration (R) obtained from a thoracic belt was acquired as well and considered as a conditioning signal in transfer entropy assessment. Synchronous sequences of 250 consecutive MCBFV, HP, MAP, SAP and R values were utilized to estimate the information genuinely transferred from MAP to MCBFV (i.e. disambiguated from R influences) and vice versa. Analogous indexes were computed from SAP to HP and vice versa. Traditional time and frequency domain analyses were carried out as well.Main results: SYNC subjects showed an increased genuine information transfer from MAP to MCBFV during TILT, while they did not exhibit the expected rise of the genuine information transfer from SAP to HP. Significance: We conclude that SYNC individuals featured an impaired cerebral autoregulation visible during TILT and were unable to activate cardiac baroreflex to cope with the postural challenge. Traditional frequency domain markers based on transfer function modulus, phase and coherence functions were less powerful or less specific in typifying the CBV and CV controls of SYNC individuals. Conditional transfer entropy approach can identify the impairment of CBV and CV controls and provide specific clues to identify subjects prone to develop postural syncope.

Sparse Causality Network Retrieval from Short Time Series

We investigate how efficiently a known underlying sparse causality structure of a simulated multivariate linear process can be retrieved from the analysis of time series of short lengths. Causality is quantified from conditional transfer entropy and the network is constructed by retaining only the statistically validated contributions. We compare results from three methodologies: two commonly used regularization methods, Glasso and ridge, and a newly introduced technique, LoGo, based on the combination of information filtering network and graphical modelling. For these three methodologies we explore the regions of time series lengths and model-parameters where a significant fraction of true causality links is retrieved. We conclude that when time series are short, with their lengths shorter than the number of variables, sparse models are better suited to uncover true causality links with LoGo retrieving the true causality network more accurately than Glasso and ridge.

Topology, Cross-Frequency, and Same-Frequency Band Interactions Shape the Generation of Phase-Amplitude Coupling in a Neural Mass Model of a Cortical Column.

Phase-amplitude coupling (PAC), a type of cross-frequency coupling (CFC) where the phase of a low-frequency rhythm modulates the amplitude of a higher frequency, is becoming an important indicator of information transmission in the brain. However, the neurobiological mechanisms underlying its generation remain undetermined. A realistic, yet tractable computational model of the phenomenon is thus needed. Here we analyze a neural mass model of a cortical column, comprising fourteen neuronal populations distributed across four layers (L2/3, L4, L5 and L6). A control analysis showed that the conditional transfer entropy (cTE) measure is able to correctly estimate the flow of information between neuronal populations. Then, we computed cTE from the phases to the amplitudes of the oscillations generated in the cortical column. This approach provides information regarding directionality by distinguishing PAC from APC (amplitude-phase coupling), i.e. the information transfer from amplitudes to phases, and can be used to estimate other types of CFC such as amplitude-amplitude coupling (AAC) and phase-phase coupling (PPC). While experiments often only focus on one or two PAC combinations (e.g., theta-gamma or alpha-gamma), we found that a cortical column can simultaneously generate almost all possible PAC combinations, depending on connectivity parameters, time constants, and external inputs. PAC interactions with and without an anatomical equivalent (direct and indirect interactions, respectively) were analyzed. We found that the strength of PAC between two populations was strongly correlated with the strength of the effective connections between the populations and, on average, did not depend on whether the PAC connection was direct or indirect. When considering a cortical column circuit as a complex network, we found that neuronal populations making indirect PAC connections had, on average, higher local clustering coefficient, efficiency, and betweenness centrality than populations making direct connections and populations not involved in PAC connections. This suggests that their interactions were more effective when transmitting information. Since approximately 60% of the obtained interactions represented indirect connections, our results highlight the importance of the topology of cortical circuits for the generation of the PAC phenomenon. Finally, our results demonstrated that indirect PAC interactions can be explained by a cascade of direct CFC and same-frequency band interactions, suggesting that PAC analysis of experimental data should be accompanied by the estimation of other types of frequency interactions for an integrative understanding of the phenomenon.

Causal conditioning and instantaneous coupling in causality graphs

This study aims at providing the definitive links between Massey and Kramer’s directed information theory and Granger causality graphs, recently formalized by Eichler. This naturally leads to consider two concepts of causality that can occur in physical systems: dynamical causality and instantaneous coupling. Although it is well accepted that the former is assessed by conditional transfer entropy, the latter is often overlooked, even if it was clearly introduced and understood in seminal studies. In the bivariate case, we show that directed information is decomposed into the sum of transfer entropy and instantaneous information exchange. In the multivariate case, encountered for conditional graph modeling, such a decomposition does not hold anymore. We provide a new insight into the problem of instantaneous coupling and show how it affects the estimated structure of a graphical model that should provide a sparse representation of a complex system. This result is discussed and analyzed for the inference of causality graphs. Two synthetic examples are developed to illustrate the theoretical concepts. Practical issues are also briefly discussed on these examples and an extension of Leonenko’s k-nearest neighbors based entropy estimators is used to derive a nonparametric estimator of directed information.