Causality detection based on information-theoretic approaches in time series analysis

Hlaváčková‐Schindler, Kateřina; Paluš, Milan; Vejmelka, Martin; Bhattacharya, Joydeep

doi:10.1016/j.physrep.2006.12.004

Cited by 677 publications

(562 citation statements)

References 191 publications

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“…Together, these expressions allow T to be written in terms of linear regression residuals, and therefore to be related directly to F . The equivalence between F and T is important because it implies that, for Gaussian variables, linear regression accounts for all the dependence among variables, further justifying CD as a measure of dynamical complexity (see [20] for a comprehensive review of nonlinear causality measures). Importantly, in the multi-variate case, the equivalence (2.8) holds for the preferred determinant version (MVGC) but not for the alternative trace version [14].…”

Section: (C) Transfer Entropymentioning

confidence: 99%

Causal density and integrated information as measures of conscious level

Seth

Barrett

Barnett

2011

Phil. Trans. R. Soc. A.

112

117

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An outstanding challenge in neuroscience is to develop theoretically grounded and practically applicable quantitative measures that are sensitive to conscious level. Such measures should be high for vivid alert conscious wakefulness, and low for unconscious states such as dreamless sleep, coma and general anaesthesia. Here, we describe recent progress in the development of measures of dynamical complexity, in particular causal density and integrated information. These and similar measures capture in different ways the extent to which a system's dynamics are simultaneously differentiated and integrated. Because conscious scenes are distinguished by the same dynamical features, these measures are therefore good candidates for reflecting conscious level. After reviewing the theoretical background, we present new simulation results demonstrating similarities and differences between the measures, and we discuss remaining challenges in the practical application of the measures to empirically obtained data.

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Section: (C) Transfer Entropymentioning

confidence: 99%

Causal density and integrated information as measures of conscious level

Seth

Barrett

Barnett

2011

Phil. Trans. R. Soc. A.

112

117

View full text Add to dashboard Cite

show abstract

“…As an alternative to linear or nonlinear parametric models, information-theoretic methods [7] constitute a valid, modelfree approach to assess nonlinear causality for both deterministic and stochastic systems. The key for assessing causality within the information-theoretic framework is to incorporate the flow of time into the desired measure through the utilization of conditional probabilities.…”

Section: Introductionmentioning

confidence: 99%

“…Another issue is related to the estimation of entropies themselves. While several estimators designed for multidimensional spaces can be applied for conditional entropy estimation [7], a common problem is the bias that increasingly affects conditional entropy estimates at augmenting dimensionality of the embedding vectors. These issues become critical when factors typical of practical applications, such as the data length and the signal-to-noise ratio, decrease to the values commonly encountered in experimental short-term time series analysis.…”

Section: Introductionmentioning

confidence: 99%

Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique

2011

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We present an approach, framed in information theory, to assess nonlinear causality between the subsystems of a whole stochastic or deterministic dynamical system. The approach follows a sequential procedure for nonuniform embedding of multivariate time series, whereby embedding vectors are built progressively on the basis of a minimization criterion applied to the entropy of the present state of the system conditioned to its past states. A corrected conditional entropy estimator compensating for the biasing effect of single points in the quantized hyperspace is used to guarantee the existence of a minimum entropy rate at which to terminate the procedure. The causal coupling is detected according to the Granger notion of predictability improvement, and is quantified in terms of information transfer. We apply the approach to simulations of deterministic and stochastic systems, showing its superiority over standard uniform embedding. Effects of quantization, data length, and noise contamination are investigated. As practical applications, we consider the assessment of cardiovascular regulatory mechanisms from the analysis of heart period, arterial pressure, and respiration time series, and the investigation of the information flow across brain areas from multichannel scalp electroencephalographic recordings.

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“…Among the variety of approaches (e.g. exploiting state-space correspondence; Arnhold et al 1999;Quiroga et al 2002), phase synchronization (Rosenblum & Pikovsky 2001;Rosenblum et al 2002) or information theory (Hlavackova-Schindler et al 2007), the cross-prediction method quantifying the predictability of one of the two series starting from samples of the other series has been widely used to assess directional coupling in short and noisy physiological time series (Schiff et al 1996;Le Van Quyen et al 1999;.…”

Section: Introductionmentioning

confidence: 99%

Assessing causality in normal and impaired short-term cardiovascular regulation via nonlinear prediction methods

Nollo

Faes

Antolini

et al. 2009

Phil. Trans. R. Soc. A.

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We investigated the ability of mutual nonlinear prediction methods to assess causal interactions in short-term cardiovascular variability during normal and impaired conditions. Directional interactions between heart period (RR interval of the ECG) and systolic arterial pressure (SAP) short-term variability series were quantified as the cross-predictability (CP) of one series given the other, and as the predictability improvement (PI ) yielded by the inclusion of samples of one series into the prediction of the other series. Nonlinear prediction was performed through global approximation (GA), approximation with locally constant models (LA0) and approximation with locally linear models (LA1) of the nonlinear function linking the samples of the two series, on patients with neurally mediated syncope and control subjects. Causality measures were evaluated in the two directions (from SAP to RR and from RR to SAP) in the supine (SU) position, in the upright position after head-up tilt (early tilt, ET) and after prolonged upright posture (late tilt, LT). While the trends for the GA, LA0 and LA1 methods were substantially superimposable, PI elicited better than CP the prevalence of causal coupling from RR to SAP during SU. Both CP and PI noted a marked decrease in coupling in both causal directions in syncope subjects during LT, documenting the impairment of cardiovascular regulation in the minutes just preceding syncope.

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Causality detection based on information-theoretic approaches in time series analysis

Cited by 677 publications

References 191 publications

Causal density and integrated information as measures of conscious level

Causal density and integrated information as measures of conscious level

Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique

Assessing causality in normal and impaired short-term cardiovascular regulation via nonlinear prediction methods

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