Detecting and quantifying causal associations in large nonlinear time series datasets

Identifying causal relationships and quantifying their strength from observational time series data are key problems in disciplines dealing with complex dynamical systems such as the Earth system or the human body. Data-driven causal inference in such systems is challenging since datasets are often high dimensional and nonlinear with limited sample sizes. Here, we introduce a novel method that flexibly combines linear or nonlinear conditional independence tests with a causal discovery algorithm to estimate causal networks from large-scale time series datasets. We validate the method on time series of well-understood physical mechanisms in the climate system and the human heart and using large-scale synthetic datasets mimicking the typical properties of real-world data. The experiments demonstrate that our method outperforms state-of-the-art techniques in detection power, which opens up entirely new possibilities to discover and quantify causal networks from time series across a range of research fields

A maximum likelihood based technique for validating detrended fluctuation analysis (ML-DFA)

Detrended Fluctuation Analysis (DFA) is widely used to assess the presence of long-range temporal correlations in time series. Signals with long-range temporal correlations are typically defined as having a power law decay in their autocorrelation function. The output of DFA is an exponent, which is the slope obtained by linear regression of a log-log fluctuation plot against window size. However, if this fluctuation plot is not linear, then the underlying signal is not self-similar, and the exponent has no meaning. There is currently no method for assessing the linearity of a DFA fluctuation plot. Here we present such a technique, called ML-DFA. We scale the DFA fluctuation plot to construct a likelihood function for a set of alternative models including polynomial, root, exponential, logarithmic and spline functions. We use this likelihood function to determine the maximum likelihood and thus to calculate values of the Akaike and Bayesian information criteria, which identify the best fit model when the number of parameters involved is taken into account and over-fitting is penalised. This ensures that, of the models that fit well, the least complicated is selected as the best fit. We apply ML-DFA to synthetic data from FARIMA processes and sine curves with DFA fluctuation plots whose form has been analytically determined, and to experimentally collected neurophysiological data. ML-DFA assesses whether the hypothesis of a linear fluctuation plot should be rejected, and thus whether the exponent can be considered meaningful. We argue that ML-DFA is essential to obtaining trustworthy results from DFA.Comment: 22 pages, 7 figure

Estimation of instantaneous complex dynamics through Lyapunov exponents: a study on heartbeat dynamics

Measures of nonlinearity and complexity, and in particular the study of Lyapunov exponents, have been increasingly used to characterize dynamical properties of a wide range of biological nonlinear systems, including cardiovascular control. In this work, we present a novel methodology able to effectively estimate the Lyapunov spectrum of a series of stochastic events in an instantaneous fashion. The paradigm relies on a novel point-process high-order nonlinear model of the event series dynamics. The long-term information is taken into account by expanding the linear, quadratic, and cubic Wiener-Volterra kernels with the orthonormal Laguerre basis functions. Applications to synthetic data such as the H�non map and R�ssler attractor, as well as two experimental heartbeat interval datasets (i.e., healthy subjects undergoing postural changes and patients with severe cardiac heart failure), focus on estimation and tracking of the Instantaneous Dominant Lyapunov Exponent (IDLE). The novel cardiovascular assessment demonstrates that our method is able to effectively and instantaneously track the nonlinear autonomic control dynamics, allowing for complexity variability estimations

Improving outcomes in interstitial lung disease through the application of bioinformatics and systems biology

Idiopathic pulmonary fibrosis (IPF) and chronic obstructive pulmonary disease (COPD) are two distinct respiratory diseases whose features including pathogenesis and progression are not fully understood. However, both clinicians utilise changes in serial pulmonary function measurements to gain an insight into disease severity and control. More accurate prediction of disease progression would be beneficial, particularly for IPF given the variability in its clinical course as an unknown factor at the time of diagnosis. Home-based, real-time monitoring of disease progression by spirometry has provided an opportunity to optimise the delivery of treatment and reduce the length of clinical trials. Therefore, the potential to understand the mechanisms underlying disease progression and generate effective treatment has been improved. In light of this, the motivation for this project is to understand the mathematical features within daily pulmonary function time series generated by IPF patients. Hopefully, statistical models of pulmonary function time series would aid the identification of significant clinical events such as acute exacerbation. The mathematical techniques used to identify potentially important features within pulmonary function time series involved the autocorrelation function, critical transitions and detrended fluctuation analysis (DFA). Temporal properties, such as the serial correlation, abrupt changes in trends and complexity, were assessed using time series from the PROFILE clinical trial and London COPD cohort. Forced vital capacity (FVC) measurements were found to be correlated to the previous day’s reading which may inform the sampling rate of lung function during clinical trials. The presence of short-term memory within FVC time series will influence the management of missing data within clinical trials, particularly methods of imputation. Also, FVC time series’ exhibit long-term memory and adaptability supporting the role of FVC as a surrogate marker for IPF disease progression.Open Acces

Complexity Variability Assessment of Nonlinear Time-Varying Cardiovascular Control

The application of complex systems theory to physiology and medicine has provided meaningful information about the nonlinear aspects underlying the dynamics of a wide range of biological processes and their disease-related aberrations. However, no studies have investigated whether meaningful information can be extracted by quantifying second-order moments of time-varying cardiovascular complexity. To this extent, we introduce a novel mathematical framework termed complexity variability, in which the variance of instantaneous Lyapunov spectra estimated over time serves as a reference quantifier. We apply the proposed methodology to four exemplary studies involving disorders which stem from cardiology, neurology and psychiatry: Congestive Heart Failure (CHF), Major Depression Disorder (MDD), Parkinson?s Disease (PD), and Post-Traumatic Stress Disorder (PTSD) patients with insomnia under a yoga training regime. We show that complexity assessments derived from simple time-averaging are not able to discern pathology-related changes in autonomic control, and we demonstrate that between-group differences in measures of complexity variability are consistent across pathologies. Pathological states such as CHF, MDD, and PD are associated with an increased complexity variability when compared to healthy controls, whereas wellbeing derived from yoga in PTSD is associated with lower time-variance of complexity

Point process time–frequency analysis of dynamic respiratory patterns during meditation practice

Respiratory sinus arrhythmia (RSA) is largely mediated by the autonomic nervous system through its modulating influence on the heart beats. We propose a robust algorithm for quantifying instantaneous RSA as applied to heart beat intervals and respiratory recordings under dynamic breathing patterns. The blood volume pressure-derived heart beat series (pulse intervals, PIs) are modeled as an inverse Gaussian point process, with the instantaneous mean PI modeled as a bivariate regression incorporating both past PIs and respiration values observed at the beats. A point process maximum likelihood algorithm is used to estimate the model parameters, and instantaneous RSA is estimated via a frequency domain transfer function evaluated at instantaneous respiratory frequency where high coherence between respiration and PIs is observed. The model is statistically validated using Kolmogorov–Smirnov goodness-of-fit analysis, as well as independence tests. The algorithm is applied to subjects engaged in meditative practice, with distinctive dynamics in the respiration patterns elicited as a result. The presented analysis confirms the ability of the algorithm to track important changes in cardiorespiratory interactions elicited during meditation, otherwise not evidenced in control resting states, reporting statistically significant increase in RSA gain as measured by our paradigm.National Institutes of Health (U.S.) (Grant R01-HL084502)National Institutes of Health (U.S.) (Grant R01-DA015644)National Institutes of Health (U.S.) (Grant DP1-OD003646)National Institutes of Health (U.S.) (Grant K01-AT00694-01

Inhomogeneous point-process entropy: an instantaneous measure of complexity in discrete systems

Measures of entropy have been widely used to characterize complexity, particularly in physiological dynamical systems modeled in discrete time. Current approaches associate these measures to finite single values within an observation window, thus not being able to characterize the system evolution at each moment in time. Here, we propose a new definition of approximate and sample entropy based on the inhomogeneous point-process theory. The discrete time series is modeled through probability density functions, which characterize and predict the time until the next event occurs as a function of the past history. Laguerre expansions of the Wiener-Volterra autoregressive terms account for the long-term nonlinear information. As the proposed measures of entropy are instantaneously defined through probability functions, the novel indices are able to provide instantaneous tracking of the system complexity. The new measures are tested on synthetic data, as well as on real data gathered from heartbeat dynamics of healthy subjects and patients with cardiac heart failure and gait recordings from short walks of young and elderly subjects. Results show that instantaneous complexity is able to effectively track the system dynamics and is not affected by statistical noise properties

Discriminating noise from chaos in heart rate variability : application to prognosis in heart failure

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 103-109).This thesis examines two challenging problems in chaos analysis: distinguishing deterministic chaos and stochastic (noise-induced) chaos, and applying chaotic heart rate variability (HRV) analysis to the prognosis of mortality in congestive heart failure (CHF). Distinguishing noise from chaos poses a major challenge in nonlinear dynamics theory since the addition of dynamic noise can make a non-chaotic nonlinear system exhibit stochastic chaos, a concept which is not well-defined and is the center of heated debate in chaos theory. A novel method for detecting dynamic noise in chaotic series is proposed in Part I of this thesis. In Part II, we show that linear and nonlinear analyses of HRV yield independent predictors of mortality. Specifically, sudden death is best predicted by frequency analysis whereas nonlinear and chaos indices are more selective for progressive pump failure death. These findings suggest a novel noninvasive probe for the clinical management of CHF patients.by Natalia M. Arzeno.M.Eng

A COMPARISION USING STATISTICAL AND MACHINE LEARNING METHODS FOR STREAMFLOW TIME SERIES

This study was carried out in the Sibinacocha lake watershed in the Peruvian Andes. In this region the long-term meteorological data are scarce and there are few studies of flow forecasts. Based on this evidence, in this study we present the monthly flow simulation, using statistical models and data-oriented model, with the purpose of evaluating the performance of these methodologies. The results of the comparative statistical analyses indicated that the data-oriented models, specifically the Recurrent Neural Networks, provided great improvements over the other models applied, specifically the ability to capture the minimum and maximum monthly flow, resulting in excellent statistical values (R2=0.85, d=0.96), thus suggesting this methodology as a possible application for flow forecasts

Assessment of cardiovascular regulation through irreversibility analysis of heart period variability: a 24 hours Holter study in healthy and chronic heart failure populations

We propose an approach based on time reversibility analysis to characterize the cardiovascular regulation and its nonlinearities as derived from 24 hours Holter recordings of heart period variability in a healthy population (n=12, age: median=43 years, range=34–55 years) and in a pathological group of age-matched chronic heart failure (CHF) patients (n=13, primarily in NYHA class II, age: median=37 years, range=33–56 years, ejection fraction: median=25%, range=13–30%). Two indices capable of detecting nonlinear irreversible dynamics according to different strategies of phase-space reconstruction (i.e. a fixed two-dimensional phase-space reconstruction and an optimal selection of the embedding dimension, respectively) are tested and compared with a more traditional nonlinear index based on local nonlinear prediction. Results showed that nonlinear dynamics owing to time irreversibility at short time scales are significantly present during daytime in healthy subjects, more frequently present in the CHF population and less frequently during night-time in both groups, thus suggesting their link with a dominant sympathetic regulation and/or with a vagal withdrawal. On the contrary, nonlinear dynamics owing to time irreversibility at longer, dominant time scales were insignificantly present in both groups. During daytime in the healthy population, irreversibility was mostly due to the presence of asymmetric patterns characterized by bradycardic runs shorter than tachycardic ones. Nonlinear dynamics produced by mechanisms different from those inducing temporal irreversibility were significantly detectable in both groups and more frequently during night-time. The present study proposes a method to distinguish different types of nonlinearities and assess their contribution over different temporal scales. Results confirm the usefulness of this method even when applied in uncontrolled experimental conditions such as those during 24 hours Holter recordings