1,721,015 research outputs found
Estimating functional networks in dynamical biological systems through convex optimization theory
Full text linkComplex systems abound in the natural and social world, e.g across systems as apparently diverse such as the human brain, the immune system, economics, and the worldwide web. Yet despite three decades of intense research activity in studying complexity, many big issues remain only partially resolved, including a good quantitative definition for a complex system. Many approaches, from time series analysis and stochastic modeling, have been proposed to model the behavior of complex systems based on observed time series by separating the systems’ behavior between observed macroscopic and hidden microscopic scales. One of the most flexible and easy to implement, in the context of linear signal processing, is the Vector Autoregressive Model (VAR) whose identification process is at the basis of the most used estimators for analyzing the statistical dependencies between different time series representing the activity of the entire dynamical system. However, the identification procedure for specific combinations of the number of processes-number of observations in the time series could lead to a severe correlation between the regressors resulting in high bias and variance in the used estimator, which can be counteracted with the use of penalized regression techniques. The first part of this thesis work has been focused on introducing and testing multivariate convex regression methodologies, as a tool for estimating the statistical dependencies among different dynamical systems. Since that there are no extensive studies available that assess the performance of different penalized regression techniques in different experimental conditions, in Chapter 1 I report a comparative analysis among different penalized regression techniques in the context of convex optimization which guarantees the existence of a solution to the VAR identification problem. Another important tool for investigating and quantifying information processing is represented by the Information theory that has already been proved to be a useful framework for the design and analysis of complex self-organized systems. In this context, it has been recently introduced a tool able to compute any measure of information dynamics from the parameters of a VAR model used to characterizes an observed multivariate Gaussian process even in combination with state-space modeling. Motivated by the fact that penalized regression techniques were not yet introduced and tested for the decomposition of information processing, Chapter 2 it is investigated the possibility to integrate the so-called LASSO regression, in a framework for the computation of these measures. The results of Chapters 1 and 2 clearly demonstrated that could be computationally very onerous, especially if combined with state-space modeling and in conditions of very long time series and dynamical systems with a very high number of processes. For this reason, in Chapter 3 we tried to overcome this computational limitation by introducing an Artificial Neural Network equivalent to a VAR model. In particular, thanks to a new training algorithm based on Stochastic gradient descent it has been possible to induce sparsity in the weights matrix of the network during the training phase, but with a less computational cost if compared with traditional LASSO implementation. This new tool was then combined with a state-space model and using for Granger causality (GC) estimation and tested on different real complex systems. Given the results of Chapters 1, 2, and 3 in Chapter 4 an extensive analysis of the performance of different methods in estimating GC, was performed. In particular, due to the high dimension of the observed data, the “curse of dimensionality” may arise leading to unreliable estimation of direct causality. With the aim of carrying out an extensive comparative study, the performance of different methodologies, available in the current literature and explored in this thesis work, for the estimation of GC have been compared. Furthermore, we provided an implementation in combination with space state models for the methods that were not previously tested with this strategy. The performance of all the methods for GC estimation combined or not with state-space models have been tested in two different simulation studies. A conclusion summarizing the main contributions of this Ph.D. project, together with their impact and limitations, closes this dissertation
Partial Information Rate Decomposition in Physiological Networks
No full textIn the field of information theory, the framework of partial information decomposition (PID) has been extensively applied to networks of two source variables sharing information with a target. A dynamic version of the PID, extended to the case of three sources and providing spectral estimates of the information shared among the involved processes, is still missing. We fill this gap by introducing a coarse-grained partial information rate decomposition (PIRD) for random processes in the time and frequency domains, applied to the network of cardiovascular, respiratory and cerebrovascular oscillations studied in patients prone to postural syncope during a protocol of postural stress
Local Granger causality
Full text linkGranger causality (GC) is a statistical notion of causal influence based on prediction via linear 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 transferred from the driver to
the target process at each discrete time point; in this frame, GC is the average of its local version. We show
that the variability of the local GC around its mean relates to the interplay between driver and innovation
(autoregressive noise) processes, and it may reveal transient instances of information transfer not detectable
from its average values. 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
Decomposing the transfer entropy to assess higher order effects in Cardiovascular Interactions
No full textTransfer Entropy (TE) can exhibit bias-either in deficiency or excess-during both pairwise and conditioned calculations, owing to high-order dependencies among the dynamic processes under consideration and the remaining processes in the system used for conditioning. To handle high order effects, instead of conditioning TE on all the measured processes except the driver and target, as in its fully conditioned version, or not conditioning at all, as in the pairwise approach, one can search for both the multiplets of variables that maximize information flow and those that minimize it, thus obtaining a decomposition of TE into unique, redundant, and synergistic atoms. This approach quantifies the relative importance of high-order effects compared to pure two-body effects while highlighting the processes that contribute to building these high-order effects alongside the driver. We employ this approach to analyze cardiovascular and cardiorespiratory interactions related to baroreflex and respiratory sinus arrhythma mechanisms
Measuring hierarchically-organized interactions in dynamic networks through spectral entropy rates: Theory, estimation, and illustrative application to physiological networks
Full text linkRecent advances in signal processing and information theory are boosting the development of new approaches for the data-driven modeling of complex network systems. In the fields of Network Physiology and Network Neuroscience where the signals of interest are rich of oscillatory content, the spectral representation of network systems is essential to ascribe interactions to specific oscillations with physiological meaning. The present work introduces a coherent framework integrating several information dynamics approaches to quantify node-specific, pairwise and higher-order interactions in network systems. A hierarchical organization of interactions of different order is established using measures of entropy rate, mutual information rate and O-information rate to quantify the dynamics of individual nodes, the links between pairs of nodes, and the redundant/synergistic hyperlinks in groups of nodes. All measures are formulated in the time domain and expanded to the spectral domain to obtain frequency-specific information. The practical computation of all measures is favored presenting a toolbox that implements parametric and non-parametric estimators and includes statistical validation approaches. The framework is illustrated using theoretical examples where the properties of the measures are displayed in benchmark simulated network systems, and representative multivariate time series in the context of Network Neuroscience and Network Physiology
Measuring Connectivity in Linear Multivariate Processes With Penalized Regression Techniques
Full text linkThe evaluation of time and frequency domain measures of coupling and causality relies on
the parametric representation of linear multivariate processes. The study of temporal dependencies among
time series is based on the identification of a Vector Autoregressive model. This procedure is pursued
through the definition of a regression problem solved by means of Ordinary Least Squares (OLS) estimator.
However, its accuracy is strongly influenced by the lack of data points and a stable solution is not always
guaranteed. To overcome this issue, it is possible to use penalized regression techniques. The aim of this
work is to compare the behavior of OLS with different penalized regression methods used for a connectivity
analysis in different experimental conditions. Bias, accuracy in the reconstruction of network structure
and computational time were used for this purpose. Different penalized regressions were tested by means
of simulated data implementing different ground-truth networks under different amounts of data samples
available. Then, the approaches were applied to real electroencephalographic signals (EEG) recorded from
a healthy volunteer performing a motor imagery task. Penalized regressions outperform OLS in simulation
settings when few data samples are available. The application on real EEG data showed how it is possible
to use features extracted from brain networks for discriminating between two tasks even in conditions of
data paucity. Penalized regression techniques can be used for brain connectivity estimation and can be
exploited for the computation of all the connectivity estimators based on linearity assumption overcoming
the limitations imposed by the classical OLS
Role of Arterial Pressure Changes on the Time-Lagged Baroreflex Response
No full textPhysiological dynamics result from the control exerted by interconnected mechanisms including causal interactions occurring at various latencies. In this work, the Partial Information Decomposition framework is exploited to investigate the causal influence of systolic arterial pressure (SAP) lagged dynamics on heart rate (HR) variations in 61 young healthy subjects undergoing the orthostatic challenge. Our results highlight how the baroreflex dynamics are mainly characterized by a fast response of the cardiac activity to arterial pressure changes and how internal SAP dynamics affect this causal interaction
Information Dynamics Analysis: A new approach based on Sparse Identification of Linear Parametric Models
No full textThe framework of information dynamics allows to quantify different aspects of the statistical structure of multivariate processes reflecting the temporal dynamics of a complex network. The information transfer from one process to another can be quantified through Transfer Entropy, and under the assumption of joint Gaussian variables it is strictly related to the concept of Granger Causality (GC). According to the most recent developments in the field, the computation of GC entails representing the processes through a Vector Autoregressive (VAR) model and a state space (SS) model typically identified by means of the Ordinary Least Squares (OLS). In this work, we propose a new identification approach for the VAR and SS models, based on Least Absolute Shrinkage and Selection Operator (LASSO), that has the advantages of maintaining good accuracy even when few data samples are available and yielding as output a sparse matrix of estimated information transfer. The performances of LASSO identification were first tested and compared to those of OLS by a simulation study and then validated on real electroencephalographic (EEG) signals recorded during a motor imagery task. Both studies indicated that LASSO, under conditions of data paucity, provides better performances in terms of network structure. Given the general nature of the model, this work opens the way to the use of LASSO regression for the computation of several measures of information dynamics currently in use in computational neuroscience
Measuring the Rate of Information Transfer in Point-Process Data: Application to Cardiovascular Interactions
No full textWe present the implementation to cardiovascular variability of a method for the information-theoretic estimation of the directed interactions between event-based data. The method allows to compute the transfer entropy rate (TER) from a source to a target point process in continuous time, thus overcoming the severe limitations associated with time discretization of event-based processes. In this work, the method is evaluated on coupled cardiovascular point processes representing the heartbeat dynamics and the related peripheral pulsation, first using a physiologically-based simulation model and then studying real point-process data from healthy subjects monitored at rest and during postural stress. Our results document the ability of TER to detect direction and strength of the interactions between cardiovascular processes, also highlighting physiologically plausible interaction mechanisms
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