Papers by Alessandro Montalto
MuTE toolbox to evaluate Multivariate Transfer Entropy
Neural networks with non-uniform embedding and explicit validation phase to assess Granger causality
Neural Networks, 2015
A challenging problem when studying a dynamical system is to find the interdependencies among its... more A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used approaches are a model-free one (transfer entropy) and a model-based one (Granger causality). Several pitfalls are related to the presence or absence of assumptions in modeling the relevant features of the data. We tried to overcome those pitfalls using a neural network approach in which a model is built without any a priori assumptions. In this sense this method can be seen as a bridge between model-free and model-based approaches. The experiments performed will show that the method presented in this work can detect the correct dynamical information flows occurring in a system of time series. Additionally we adopt a non-uniform embedding framework according to which only the past states that actually help the prediction are entered into the model, improving the prediction and avoiding the risk of overfitting. This method also leads to a further improvement with respect to traditional Granger causality approaches when redundant variables (i.e. variables sharing the same information about the future of the system) are involved. Neural networks are also able to recognize dynamics in data sets completely different from the ones used during the training phase.
PLOS ONE, 2015
An analysis of cardiorespiratory dynamics during mental arithmetic, which induces stress, and sus... more An analysis of cardiorespiratory dynamics during mental arithmetic, which induces stress, and sustained attention was conducted using information theory. The information storage and internal information of heart rate variability (HRV) were determined respectively as the self-entropy of the tachogram, and the self-entropy of the tachogram conditioned to the knowledge of respiration. The information transfer and cross information from respiration to HRV were assessed as the transfer and cross-entropy, both measures of cardiorespiratory coupling. These information-theoretic measures identified significant nonlinearities in the cardiorespiratory time series. Additionally, it was shown that, although mental stress is related to a reduction in vagal activity, no difference in cardiorespiratory coupling was found when several mental states (rest, mental stress, sustained attention) are compared. However, the self-entropy of HRV conditioned to respiration was very informative to study the predictability of RR interval series during mental tasks, and showed higher predictability during mental arithmetic compared to sustained attention or rest.
A challenge for physiologists and neuroscientists is to map information transfer between componen... more A challenge for physiologists and neuroscientists is to map information transfer between components of the systems that they study at different scales, in order to derive important knowledge on structure and function from the analysis of the recorded dynamics. The components of physiological networks often interact in a nonlinear way and through mechanisms which are in general not completely known. It is then safer that the method of choice for analyzing these interactions does not rely on any model or assumption on the nature of the data and their interactions. Transfer entropy has emerged as a powerful tool to quantify directed dynamical interactions. In this paper we compare different approaches to evaluate transfer entropy, some of them already proposed, some novel, and present their implementation in a freeware MATLAB toolbox. Applications to simulated and real data are presented.
Information decomposition of short-term cardiovascular and cardiorespiratory variability
ABSTRACT We present an entropy decomposition strategy aimed at quantifying how the predictive inf... more ABSTRACT We present an entropy decomposition strategy aimed at quantifying how the predictive information (PI) about heart rate (HR) variability is dynamically stored in HR and is transferred to HR from arterial pressure (AP) and respiration (RS) variability according to synergistic or redundant cooperation. The PI is expressed as the sum of the self entropy (SE) of HR plus the transfer entropy (TE) from {RS,AP} to HR, quantifying respectively the information stored in the cardiac system and transferred to the cardiac system to the vascular and respiratory systems. The information transfer is further decomposed as the sum of the (unconditioned) TE from RS to HR plus the TE from SP to HR conditioned to RS. Moreover a redundancy/synergy measure is defined as the difference between unconditioned and conditioned TE from RS to HR. We show that, under the linear Gaussian assumption for the underlying multiple processes, all the proposed information dynamical measures can be calculated analytically, and present a method for their computation from the parameters of a vector autoregressive model. The method is then evaluated on a simulated process reproducing realistic HR, AP and RS rhythms, showing how known cardiovascular and cardiorespiratory mechanisms can be characterized in terms of the proposed information decomposition measures.
MuTE: a new MATLAB toolbox for estimating the multivariate transfer entropy in physiological variability series
ABSTRACT We present a new time series analysis toolbox, developed in Matlab, for the estimation o... more ABSTRACT We present a new time series analysis toolbox, developed in Matlab, for the estimation of the Transfer entropy (TE) between time series taken from a multivariate dataset. The main feature of the toolbox is its fully multivariate implementation, that is made possible by the design of an approach for the non-uniform embedding (NUE) of the observed time series. The toolbox is equipped with parametric (linear) and non-parametric (based on binning or nearest neighbors) entropy estimators. All these estimators, implemented using the NUE approach in comparison with the classical approach based on uniform embedding, are tested on RR interval, systolic pressure and respiration variability series measured from healthy subjects during head-up tilt. The results support the necessity of resorting to NUE for obtaining reliable estimates of the multivariate TE in short-term cardiovascular and cardiorespiratory variability.
Comparing model-free and model-based transfer entropy estimators in cardiovascular variability
ABSTRACT Information flow between heart period (T), systolic pressure (S) and respiration (R) var... more ABSTRACT Information flow between heart period (T), systolic pressure (S) and respiration (R) variability in a head-up tilt (HUT) protocol is assessed by transfer entropy (TE). Two estimates of TE are compared: the model-based (MB) approach using linear regression under the Gaussian assumption, and the model-free (MF) approach combining binning estimates of entropy and non-uniform delay embedding. The approaches were applied to 300-beats series of T, S, R measured in the supine (su) and upright (up) positions during HUT. Both MB and MF approaches detected a unidirectional information transfer from R to T and from R to S, and a significant decrease of the TE from R to T, as well as a significant increase of the TE from S to T, moving from su to up. For the MF approach, these trends were supported by the statistical test for TE significance. These results suggest that TE estimated from T, S and R variability can successfully describe the physiological mechanisms involved in the short term cardiovascular and cardiorespiratory regulation during HUT.
In the study of interacting physiological systems, model-free tools for time series analysis are ... more In the study of interacting physiological systems, model-free tools for time series analysis are fundamental to provide a proper description of how the coupling among systems arises from the multiple involved regulatory mechanisms. This study presents an approach which evaluates direction, magnitude and exact timing of the information transfer between two time series belonging to a multivariate data set. The approach performs a decomposition of the well known transfer entropy (TE) which achieves (i) identifying, according to a lag-specific information-theoretic formulation of the concept of Granger causality, the set of time lags associated with significant information transfer, and (ii) assigning to these delays an amount of information transfer such that the total contribution yields the aggregate TE. The approach is first validated on realizations of simulated linear and nonlinear multivariate processes interacting at different time lags and with different strength, reporting a high accuracy in the detection of imposed delays, and showing that the estimated lag-specific TE follows the imposed coupling strength. The subsequent application to heart period, systolic arterial pressure and respiration variability series measured from healthy subjects during a tilt test protocol illustrated how the proposed approach quantifies the modifications in the involvement and latency of important mechanisms of short-term physiological regulation, like the baroreflex and the respiratory sinus arrhythmia, induced by the orthostatic stress.
Information dynamics in cardiorespiratory analyses: Application to controlled breathing
Voluntary adjustment of the breathing pattern is widely used to deal with stress-related conditio... more Voluntary adjustment of the breathing pattern is widely used to deal with stress-related conditions. In this study, effects of slow and fast breathing with a low and high inspiratory to expiratory time on heart rate variability (HRV) are evaluated by means of information dynamics. Information transfer is quantified both as the traditional transfer entropy as well as the cross entropy, where the latter does not condition on the past of HRV, thereby taking the highly unidirectional relation between respiration and heart rate into account. The results show that the cross entropy is more suited to quantify cardiorespiratory information transfer as this measure increases during slow breathing, indicating the increased cardiorespiratory coupling and suggesting the shift towards vagal activation during slow breathing. Additionally we found that controlled breathing, either slow or fast, results as well in an increase in cardiorespiratory coupling, compared to spontaneous breathing, which demonstrates the beneficial effects of instructed breathing.
Interictal cardiorespiratory variability in temporal lobe and absence epilepsy in childhood
It is well known that epilepsy has a profound effect on the autonomic nervous system, especially ... more It is well known that epilepsy has a profound effect on the autonomic nervous system, especially on the autonomic control of heart rate and respiration. This effect has been widely studied during seizure activity, but less attention has been given to interictal (i.e. seizure-free) activity. The studies that have been done on this topic, showed that heart rate and respiration can be affected individually, even without the occurrence of seizures. In this work, the interactions between these two individual physiological variables are analysed during interictal activity in temporal lobe and absence epilepsy in childhood. These interactions are assessed by decomposing the predictive information about heart rate variability, into different components like the transfer entropy, cross-entropy, self- entropy and the conditional self entropy. Each one of these components quantifies different types of shared information. However, when using the cross-entropy and the conditional self entropy, it is possible to split the information carried by the heart rate, into two main components, one related to respiration and one related to different mechanisms, like sympathetic activation. This can be done after assuming a directional link going from respiration to heart rate. After analysing all the entropy components, it is shown that in subjects with absence epilepsy the information shared by respiration and heart rate is significantly lower than for normal subjects. And a more remarkable finding indicates that this type of epilepsy seems to have a long term effect on the cardiac and respiratory control mechanisms of the autonomic nervous system.
Information dynamics in cardiorespiratory time series during mental stress testing
ABSTRACT In this study, we assessed the information dynamics of respiration and heart rate variab... more ABSTRACT In this study, we assessed the information dynamics of respiration and heart rate variability during mental stress testing by means of the cross-entropy, a measure of cardiorespiratory coupling, and the self-entropy of the tachogram conditioned to the knowledge of respiration. Although stress is related to a reduction in vagal activity, no difference in cardiorespiratory coupling was found when 5 minutes of rest and stress were compared. The conditional self-entropy, on the other hand, showed significantly higher values during stress, indicating a higher predictability of the tachogram. These results show that entropy analyses of cardiorespiratory data reveal new information that could not be obtained with traditional heart rate variability studies.
Drafts by Alessandro Montalto
The following project concerns a new way human beings can communicate feelings without the filter... more The following project concerns a new way human beings can communicate feelings without the filter of words. Our idea is based on information theory and data mining approaches. Thinking about a person as a point in a multidimensional space, we would like to develop a program consisting of two main steps: the first one dealing with the choice of the dimensions better able to represent a person; the second one concerning a classifier that can handle the multidimensional space previously chosen to give informations about the current emotional state of a person. The result will be a device able to interpret in real time, after an appropriate training, the emotions experienced by a person who receives an external input, measuring quantities, related to the spontaneous and unconscious brain and body reactions to the stimulus, such as heart beat rate, arterial pressure, facial expression and so on. The aim is not only to give people a better and deeper understanding of themselves and their loved one, but also a completely new way to communicate which only requires the act to " feel " and the willing to share. Moreover the device will be useful to detect personality disorders in early stages if users' data are collected in a big anonymous database because of the predictable behaviour that the machine learning techniques have.
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Papers by Alessandro Montalto
Drafts by Alessandro Montalto