arXiv subjects

Yuri Antonacci

Publications and source records attributed to Yuri Antonacci.

16 recordsLinked to original sources

arXiv2026

From Statistical to Structural Synergy: A Predictability Framework to Quantify the Effects due to High-Order Mechanisms

High-order interactions are increasingly recognized as a hallmark of collective dynamics in complex systems. The relationship between high-order behaviours (HOBs), observed as synergistic or redundant statistical dependencies, and high-order mechanisms (HOMs), related to the structural or dynamical rules of the data-generating process, remains difficult to establish from data. We introduce a predictability-based framework to disentangle these two levels of description in complex network systems. Structural synergy is defined as the excess predictive power gained when two sources are considered jointly beyond the best additive description and is estimated through polynomial regression by comparing a model with interaction terms against an additive model. Simulations show that dependencies among sources reflecting HOBs can arise even in the absence of HOMs, while synergy due to a non-additive mechanism may remain hidden when the observed synergy-redundancy balance is dominated by redundancy and become detectable only through structural synergy. Applications to climate and source-reconstructed cortical EEG dynamics reveal significant non-additive predictive components despite predominantly redundancy-dominated HOBs. These findings emphasize that HOBs and HOMs can dissociate: a system may display redundancy-dominated HOBs while still containing a significant synergistic mechanism. The proposed framework supports a mechanistically informed interpretation of complex-system dynamics and may help to identify when mechanism-based models are needed to predict the response of a system to perturbations or interventions, while also recognizing that structural synergy should be interpreted as evidence of non-additive predictive structure rather than as a direct identification of the underlying generative mechanism.

stat.ME↗

arXiv2026

Dissecting Spectral Granger Causality through Partial Information Decomposition

Granger causality (GC), a popular statistical method for the inference of directional influences between time series measured from a complex network, is sensitive to high-order (non-pairwise) interactions which fundamentally shape the collective network dynamics. This work introduces Partial Decomposition of Granger Causality (PDGC), a tool eliciting redundant and synergistic causal interactions in the pattern of information flow between the subsystems of physiological networks. The tool exploits the framework of partial information decomposition to dissect the multivariate GC from a set of driver random processes to a target process into unique effects carried exclusively by each driver, redundant effects carried identically by more drivers, and synergistic effects carried jointly by some drivers but not by any of them individually. Computation is based on multivariate state-space models expanded in the frequency domain to assess PDGC both in specific bands of physiological interest and in the time domain after whole-band integration. The validation on benchmark simulations demonstrates that the measures of unique, redundant, and synergistic GC reflect the underlying causal mechanisms and are computationally reliable. The application to arterial pressure, respiration, cerebral blood velocity and heart period variability reveals striking differences in the response to postural stress of patients prone to neurally-mediated syncope compared to healthy controls. The extraction of high-order causality patterns from the spectral GC favors dissecting the mechanisms of causal influence underlying multivariate interactions among oscillatory processes in many data-driven applications of network science.

stat.ME↗

arXiv2025

Redundant and synergistic interactions in a complex network of single-transistor electronic chaotic oscillators and in neurophysiological recordings

Complex networks often exhibit emergent behaviors, where simple dyadic interactions yield collective dynamics that cannot be explained by examining the system's units individually or in pairs. Understanding how redundant and synergistic interaction emerges from elementary connectivity patterns is important in characterizing the behavior of physical, biological, and engineering systems. In this study, the information-theoretic framework of Partial Information Decomposition (PID) is employed to investigate how pairs of signals measured at the nodes of large network systems contribute individually and in cooperation with each other to determine the overall state of the network. The analyzed systems are networks of numerically simulated Roessler oscillators and physical single-transistor electronic chaotic oscillators, reproducing purely pairwise and symmetric links in biological neuronal cultures, and cortical electroencephalographic networks assessed in humans. In the two settings, PID was extensively applied to decompose the information brought by pairs of signals to the overall state of the system, assessed respectively as the dynamic regime (from asynchronous chaos to synchronization) and the subject condition (open vs. closed eyes). Our approach highlights the coexistence of redundant and synergistic interplay in determining the effect of the pairwise dynamics on the system's state. Specifically, we demonstrate how, in a highly synchronized system, where units act following overlapped redundant behaviors, their joint consideration helps determine the system's state though their synergistic interactions. Our findings reveal the emergence of non-trivial behaviors in networked system based on pairwise connections and straightforward neural states, highlighting the need for using appropriate analytical tools to capture complex phenomena.

nlin.CD↗

arXiv2025

Investigating High-Order Behaviors in Multivariate Cardiovascular Interactions via Nonlinear Prediction and Information-Theoretic Tools

Assessing the synergistic high-order behaviors (HOBs) that emerge from underlying structural mechanisms is crucial to characterize complex systems. This work leverages the combined use of predictability and information measures to detect and quantify HOBs in synthetic and physiological network systems. After providing formal definitions of mechanisms and behaviors in a complex system, measures of statistical synergy are defined as the whole-minus-sum excess of mutual predictability ($\Delta_\textrm{MP}$) or mutual information ($\Delta_\textrm{MI}$) obtained when considering the system as a whole rather than as a combination of its units. The two measures are computed using model-free methods based on nonlinear prediction and entropy estimation. The application to simulated linear Gaussian systems and nonlinear deterministic and stochastic dynamic systems shows that $\Delta_\textrm{MP}$ tends to vanish for target variables influenced by additive effects of single independent source variables and is positive in the presence of group interactions between sources, while $\Delta_\textrm{MI}$ exhibits a higher propensity to display positive values. The analysis of physiological variables shows significant values of $\Delta_\textrm{MI}$ when investigating the additive effect of systolic and diastolic arterial pressure on mean arterial pressure, and of both $\Delta_\textrm{MP}$ and $\Delta_\textrm{MI}$ when assessing how diastolic pressure is modulated by pre-ejection and left-ventricular ejection times. HOBs can be more clearly identified by information-theoretic measures, while prediction measures are more sensitive to synergy arising from the governing rules of the system analyzed rather than from pure statistical dependencies. Quantifying HOBs through measures sensitive to structural mechanisms can provide biomarkers to assess physio-pathological alterations of cardiovascular networks.

q-bio.QM↗

arXiv2025

A Method for the Time-Frequency Analysis of High-Order Interactions in Non-Stationary Physiological Networks

Several data-driven approaches based on information theory have been proposed for analyzing high-order interactions involving three or more components of a network system. Most of these methods are defined only in the time domain and rely on the assumption of stationarity in the underlying dynamics, making them inherently unable to detect frequency-specific behaviors and track transient functional links in physiological networks. This study introduces a new framework which enables the time-varying and time-frequency analysis of high-order interactions in network of random processes through the spectral representation of vector autoregressive models. The time- and frequency-resolved analysis of synergistic and redundant interactions among groups of processes is ensured by a robust identification procedure based on a recursive least squares estimator with a forgetting factor. Validation on simulated networks illustrates how the time-frequency analysis is able to highlight transient synergistic behaviors emerging in specific frequency bands which cannot be detected by time-domain stationary analyses. The application on brain evoked potentials in rats elicits the presence of redundant information timed with whisker stimulation and mostly occurring in the contralateral hemisphere. The proposed framework enables a comprehensive time-varying and time-frequency analysis of the hierarchical organization of dynamic networks. As our approach goes beyond pairwise interactions, it is well suited for the study of transient high-order behaviors arising during state transitions in many network systems commonly studied in physiology, neuroscience and other fields.

stat.AP↗

arXiv2025

Partial Information Rate Decomposition

Partial Information Decomposition (PID) is a principled and flexible method to unveil complex high-order interactions in multi-unit network systems. Though being defined exclusively for random variables, PID is ubiquitously applied to multivariate time series taken as realizations of random processes with temporal statistical structure. Here, to overcome the incorrect depiction of high-order effects by PID schemes applied to dynamic networks, we introduce the framework of Partial Information Rate Decomposition (PIRD). PIRD is first formalized applying lattice theory to decompose the information shared dynamically between a target random process and a set of source processes, and then implemented for Gaussian processes through a spectral expansion of information rates. The new framework is validated in simulated network systems and demonstrated in the practical analysis of time series from large-scale climate oscillations.

stat.ME↗

arXiv2025

Decomposing Multivariate Information Rates in Networks of Random Processes

The Partial Information Decomposition (PID) framework has emerged as a powerful tool for analyzing high-order interdependencies in complex network systems. However, its application to dynamic processes remains challenging due to the implicit assumption of memorylessness, which often falls in real-world scenarios. In this work, we introduce the framework of Partial Information Rate Decomposition (PIRD) that extends PID to random processes with temporal correlations. By leveraging mutual information rate (MIR) instead of mutual information (MI), our approach decomposes the dynamic information shared by multivariate random processes into unique, redundant, and synergistic contributions obtained aggregating information rate atoms in a principled manner. To solve PIRD, we define a pointwise redundancy rate function based on the minimum MI principle applied locally in the frequency-domain representation of the processes. The framework is validated in benchmark simulations of Gaussian systems, demonstrating its advantages over traditional PID in capturing temporal correlations and showing how the spectral representation may reveal scale-specific higher-order interactions that are obscured in the time domain. Furthermore, we apply PIRD to a physiological network comprising cerebrovascular and cardiovascular variables, revealing frequency-dependent redundant information exchange during a protocol of postural stress. Our results highlight the necessity of accounting for the full temporal statistical structure and spectral content of vector random processes to meaningfully perform information decomposition in network systems with dynamic behavior such as those typically encountered in neuroscience and physiology.

stat.ME↗

arXiv2024

Partial information decomposition for mixed discrete and continuous random variables

The framework of Partial Information Decomposition (PID) unveils complex nonlinear interactions in network systems by dissecting the mutual information (MI) between a target variable and several source variables. While PID measures have been formulated mostly for discrete variables, with only recent extensions to continuous systems, the case of mixed variables where the target is discrete and the sources are continuous is not yet covered properly. Here, we introduce a PID scheme whereby the MI between a specific state of the discrete target and (subsets of) the continuous sources is expressed as a Kullback-Leibler divergence and is estimated through a data-efficient nearest-neighbor strategy. The effectiveness of this PID is demonstrated in simulated systems of mixed variables and showcased in a physiological application. Our approach is relevant to many scientific problems, including sensory coding in neuroscience and feature selection in machine learning.

physics.data-an↗

arXiv2024

Network Representation of Higher-Order Interactions Based on Information Dynamics

Many complex systems in science and engineering are modeled as networks whose nodes and links depict the temporal evolution of each system unit and the dynamic interaction between pairs of units, which are assessed respectively using measures of auto- and cross-correlation or variants thereof. However, a growing body of work is documenting that this standard network representation can neglect potentially crucial information shared by three or more dynamic processes in the form of higher-order interactions (HOIs). While several measures, mostly derived from information theory, are available to assess HOIs in network systems mapped by multivariate time series, none of them is able to provide a compact and detailed representation of higher-order interdependencies. In this work, we fill this gap by introducing a framework for the assessment of HOIs in dynamic network systems at different levels of resolution. The framework is grounded on the dynamic implementation of the O-information, a new measure assessing HOIs in dynamic networks, which is here used together with its local counterpart and its gradient to quantify HOIs respectively for the network as a whole, for each link, and for each node. The integration of these measures into the conventional network representation results in a tool for the representation of HOIs as networks, which is defined formally using measures of information dynamics, implemented in its linear version by using vector regression models and statistical validation techniques, illustrated in simulated network systems, and finally applied to an illustrative example in the field of network physiology.

stat.ME↗

arXiv2024

Measuring hierarchically-organized interactions in dynamic networks through spectral entropy rates: theory, estimation, and illustrative application to physiological networks

Recent advances in signal processing and information theory are boosting the development of new approaches for the data-driven modelling of complex network systems. In the fields of Network Physiology and Network Neuroscience where the signals of interest are often rich of oscillatory content, the spectral representation of network systems is essential to ascribe the analyzed interactions to specific oscillations with physiological meaning. In this context, the present work formalizes a coherent framework which integrates several information dynamics approaches to quantify node-specific, pairwise and higher-order interactions in network systems. The framework establishes a hierarchical organization of interactions of different order using measures of entropy rate, mutual information rate and O-information rate, to quantify respectively the dynamics of individual nodes, the links between pairs of nodes, and the redundant/synergistic hyperlinks between groups of nodes. All measures are formulated in the time domain, and then expanded to the spectral domain to obtain frequency-specific information. The practical computation of all measures is favored presenting a toolbox that implements their parametric and non-parametric estimation, and includes approaches to assess their statistical significance. The framework is illustrated first using theoretical examples where the properties of the measures are displayed in benchmark simulated network systems, and then applied to representative examples of multivariate time series in the context of Network Neuroscience and Network Physiology.

stat.ME↗

arXiv2024

Assessing High-Order Links in Cardiovascular and Respiratory Networks via Static and Dynamic Information Measures

The network representation is becoming increasingly popular for the description of cardiovascular interactions based on the analysis of multiple simultaneously collected variables. However, the traditional methods to assess network links based on pairwise interaction measures cannot reveal high-order effects involving more than two nodes, and are not appropriate to infer the underlying network topology. To address these limitations, here we introduce a framework which combines the assessment of high-order interactions with statistical inference for the characterization of the functional links sustaining physiological networks. The framework develops information-theoretic measures quantifying how two nodes interact in a redundant or synergistic way with the rest of the network, and employs these measures for reconstructing the functional structure of the network. The measures are implemented for both static and dynamic networks mapped respectively by random variables and random processes using plug-in and model-based entropy estimators. The validation on theoretical and numerical simulated networks documents the ability of the framework to represent high-order interactions as networks and to detect statistical structures associated to cascade, common drive and common target effects. The application to cardiovascular networks mapped by the beat-to-beat variability of heart rate, respiration, arterial pressure, cardiac output and vascular resistance allowed noninvasive characterization of several mechanisms of cardiovascular control operating in resting state and during orthostatic stress. Our approach brings to new comprehensive assessment of physiological interactions and complements existing strategies for the classification of pathophysiological states.

stat.ME↗

arXiv2023

A method to assess Granger causality, isolation and autonomy in the time and frequency domains: theory and application to cerebrovascular variability

Concepts of Granger causality (GC) and Granger autonomy (GA) are central to assess the dynamics of coupled physiologic processes. While causality measures have been already proposed and applied in time and frequency domains, measures quantifying self-dependencies are still limited to the time-domain formulation and lack of a clear spectral representation. We embed into the classical linear parametric framework for computing GC from a driver random process X to a target process Y a measure of Granger Isolation (GI) quantifying the part of the dynamics of Y not originating from X, and a new spectral measure of GA assessing frequency-specific patterns of self-dependencies in Y. The measures are illustrated in theoretical simulations and applied to time series of mean arterial pressure and cerebral blood flow velocity obtained in subjects prone to develop postural syncope and healthy controls. Simulations show that GI is complementary to GC but not trivially related to it, while GA reflects the regularity of the internal dynamics of the analyzed target process. In the application to cerebrovascular interactions, spectral GA quantified the physiological response to postural stress of slow cerebral blood flow oscillations, while spectral GC and GI detected an altered response to postural stress in subjects prone to syncope, likely related to impaired cerebral autoregulation. The new spectral measures of GI and GA are useful complements to GC for the analysis of interacting oscillatory processes, and detect physiological and pathological responses to postural stress which cannot be traced in the time domain. The assessment of causality, isolation and autonomy opens new perspectives for the analysis of coupled biological processes in both physiological and clinical investigations.

eess.SP↗

arXiv2022

Gradients of O-information: low-order descriptors of high-order dependencies

O-information is an information-theoretic metric that captures the overall balance between redundant and synergistic information shared by groups of three or more variables. To complement the global assessment provided by this metric, here we propose the gradients of the O-information as low-order descriptors that can characterise how high-order effects are localised across a system of interest. We illustrate the capabilities of the proposed framework by revealing the role of specific spins in Ising models with frustration, and on practical data analysis on US macroeconomic data. Our theoretical and empirical analyses demonstrate the potential of these gradients to highlight the contribution of variables in forming high-order informational circuits

cs.IT↗

arXiv2022

A Framework for the Time- and Frequency-Domain Assessment of High-Order Interactions in Brain and Physiological Networks

While the standard network description of complex systems is based on quantifying links between pairs of system units, higher-order interactions (HOIs) involving three or more units play a major role in governing the collective network behavior. This work introduces an approach to quantify pairwise and HOIs for multivariate rhythmic processes interacting across multiple time scales. We define the so-called O-information rate (OIR) as a new metric to assess HOIs for multivariate time series, and propose a framework to decompose it into measures quantifying Granger-causal and instantaneous influences, as well as to expand it in the frequency domain. The framework exploits the spectral representation of vector autoregressive and state-space models to assess synergistic and redundant interactions among groups of processes, both in specific bands and in the time domain after whole-band integration. Validation on simulated networks illustrates how the spectral OIR can highlight redundant and synergistic HOIs emerging at specific frequencies but not using time-domain measures. The application to physiological networks described by heart period, arterial pressure and respiration measured in healthy subjects during paced breathing, and to brain networks described by ECoG signals acquired in an animal experiment during anesthesia, document the capability of our approach to identify informational circuits relevant to well-defined cardiovascular oscillations and brain rhythms and related to specific physiological mechanisms of autonomic control and altered consciousness. The proposed framework allows a hierarchically-organized evaluation of time- and frequency-domain interactions in networks mapped by multivariate time series, and its high flexibility and scalability make it suitable to investigate networks beyond pairwise interactions in neuroscience, physiology and other fields.

stat.ME↗

arXiv2020

An information-theoretic framework to measure the dynamic interaction between neural spike trains

Understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience. However, an optimal approach of assessing these interactions has not been established, as existing methods either do not consider the inherent point process nature of spike trains or are based on parametric assumptions that may lead to wrong inferences if not met. This work presents a framework, grounded in the field of information dynamics, for the model-free, continuous-time estimation of both undirected (symmetric) and directed (causal) interactions between pairs of spike trains. The framework decomposes the overall information exchanged dynamically between two point processes X and Y as the sum of the dynamic mutual information (dMI) between the histories of X and Y, plus the transfer entropy (TE) along the directions X->Y and Y->X. Building on recent work which derived theoretical expressions and consistent estimators for the TE in continuous time, we develop algorithms for estimating efficiently all measures in our framework through nearest neighbor statistics. These algorithms are validated in simulations of independent and coupled spike train processes, showing the accuracy of dMI and TE in the assessment of undirected and directed interactions even for weakly coupled and short realizations, and proving the superiority of the continuous-time estimator over the discrete-time method. Then, the usefulness of the framework is illustrated in a real data scenario of recordings from in-vitro preparations of spontaneously-growing cultures of cortical neurons, where we show the ability of dMI and TE to identify how the networks of undirected and directed spike train interactions change their topology through maturation of the neuronal cultures.

q-bio.NC↗

arXiv2020

Local Granger Causality

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes. We exploit such equivalence and calculate exactly the 'local Granger causality', i.e. the profile of the information transfer at each discrete time point in Gaussian processes; in this frame Granger causality is the average of its local version. Our approach offers a robust and computationally fast method to follow the information transfer along the time history of linear stochastic processes, as well as of nonlinear complex systems studied in the Gaussian approximation.

q-bio.QM↗