scholarly journals Detecting Causality in Multivariate Time Series via Non-Uniform Embedding

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1233 ◽  
Author(s):  
Ziyu Jia ◽  
Youfang Lin ◽  
Zehui Jiao ◽  
Yan Ma ◽  
Jing Wang
Keyword(s):  
Time Series ◽  
Mutual Information ◽  
Chaotic Systems ◽  
Multivariate Time Series ◽  
Conditional Mutual Information ◽  
Uniform Embedding ◽  
Actual Application ◽  
Dimensional Approximation ◽  
Coupling Strengths ◽  
Low Dimensional

Causal analysis based on non-uniform embedding schemes is an important way to detect the underlying interactions between dynamic systems. However, there are still some obstacles to estimating high-dimensional conditional mutual information and forming optimal mixed embedding vector in traditional non-uniform embedding schemes. In this study, we present a new non-uniform embedding method framed in information theory to detect causality for multivariate time series, named LM-PMIME, which integrates the low-dimensional approximation of conditional mutual information and the mixed search strategy for the construction of the mixed embedding vector. We apply the proposed method to simulations of linear stochastic, nonlinear stochastic, and chaotic systems, demonstrating its superiority over partial conditional mutual information from mixed embedding (PMIME) method. Moreover, the proposed method works well for multivariate time series with weak coupling strengths, especially for chaotic systems. In the actual application, we show its applicability to epilepsy multichannel electrocorticographic recordings.

scholarly journals Computation in a Single Neuron: Hodgkin and Huxley Revisited

2003 ◽  
Vol 15 (8) ◽  
pp. 1715-1749 ◽  
Author(s):  
Blaise Agüera y Arcas ◽  
Adrienne L. Fairhall ◽  
William Bialek
Keyword(s):  
Mutual Information ◽  
Feature Detection ◽  
Dimensional Space ◽  
Model Neuron ◽  
Realistic Model ◽  
High Time Resolution ◽  
Correlation Technique ◽  
Two Dimensional ◽  
Dimensional Approximation ◽  
Low Dimensional

A spiking neuron “computes” by transforming a complex dynamical input into a train of action potentials, or spikes. The computation performed by the neuron can be formulated as dimensional reduction, or feature detection, followed by a nonlinear decision function over the low-dimensional space. Generalizations of the reverse correlation technique with white noise input provide a numerical strategy for extracting the relevant low-dimensional features from experimental data, and information theory can be used to evaluate the quality of the low-dimensional approximation. We apply these methods to analyze the simplest biophysically realistic model neuron, the Hodgkin-Huxley (HH) model, using this system to illustrate the general methodological issues. We focus on the features in the stimulus that trigger a spike, explicitly eliminating the effects of interactions between spikes. One can approximate this triggering “feature space” as a two-dimensional linear subspace in the high-dimensional space of input histories, capturing in this way a substantial fraction of the mutual information between inputs and spike time. We find that an even better approximation, however, is to describe the relevant subspace as two dimensional but curved; in this way, we can capture 90% of the mutual information even at high time resolution. Our analysis provides a new understanding of the computational properties of the HH model. While it is common to approximate neural behavior as “integrate and fire,” the HH model is not an integrator nor is it well described by a single threshold.

Validity of Dimensional Complexity Measures of EEG Signals

1997 ◽  
Vol 07 (01) ◽  
pp. 173-186 ◽  
Author(s):  
N. Pradhan ◽  
P. K. Sadasivan
Keyword(s):  
Time Series ◽  
Gaussian Noise ◽  
Chaotic Systems ◽  
Surrogate Data ◽  
Data Sets ◽  
Eeg Signals ◽  
Complexity Measures ◽  
Dimensional Complexity ◽  
Colored Gaussian Noise ◽  
Low Dimensional

The measure of dimensional complexity has the potential for feature extraction, modeling and prediction of EEG signals. However, the nonlinear dynamics of neuronal processes is under criticism that EEG signals may have a simpler stochastic description and chaotic dynamical measures of EEG may be spurious or unnecessary. Surrogate-data testing has been propounded to detect nonlinearity and chaos in experimental time series and to differentiate it from linear stochastic processes or colored noises. The surrogate data tests of brain signals (EEG) have produced equivocal results. Therefore, we examine the surrogate testing procedure using numerical data of classical chaotic systems, mixed sine waves, white Gaussian and colored Gaussian noises and typical EEGs. White Gaussian noise and classical chaotic time series are easily discerned by the surrogate-data test. However, a colored Gaussian noise data of low correlation dimensions (D2) or mixed sine waves containing less number of sinusoids show behaviors similar to the low dimensional deterministic chaotic systems. There are significant differences in D2 values between the original and surrogate data sets. The colored Gaussian noise appears linear and stochastic only when there is an increased randomness in its pattern and the signal is high dimensional. Our results clearly indicate that the "surrogate testing" alone may not be a sufficient test for distinguishing colored noises from low dimensional chaos. The EEG time series produce finite correlation dimensions. The surrogate testing of 8 independent realizations of different forms of EEG activities produce significantly different D2 values than the original data sets. Apparently many natural phenomena follow deterministic chaos and as the dimensional complexity of the system increases (D2 > 5) it may approximate a stochastic process. Thus EEG appears unlikely to have originated from a linear system driven by white noise.

scholarly journals Multivariate time series prediction of high dimensional data based on deep reinforcement learning

2021 ◽  
Vol 256 ◽  
pp. 02038
Author(s):  
Xin Ji ◽  
Haifeng Zhang ◽  
Jianfang Li ◽  
Xiaolong Zhao ◽  
Shouchao Li ◽  
...  
Keyword(s):  
Time Series ◽  
Reinforcement Learning ◽  
Phase Space ◽  
Time Series Prediction ◽  
Multivariate Time Series ◽  
High Dimensional Data ◽  
Prediction Method ◽  
Conditional Entropy ◽  
High Dimensional ◽  
Low Dimensional

In order to improve the prediction accuracy of high-dimensional data time series, a high-dimensional data multivariate time series prediction method based on deep reinforcement learning is proposed. The deep reinforcement learning method is used to solve the time delay of each variable and mine the data characteristics. According to the principle of maximum conditional entropy, the embedding dimension of the phase space is expanded, and a multivariate time series model of high-dimensional data is constructed. Thus, the conversion of reconstructed coordinates from low-dimensional to high-dimensional can be kept relatively stable. The strong independence and low redundancy of the final reconstructed phase space construct an effective model input vector for multivariate time series forecasting. Numerical experiments of classical multivariable chaotic time series show that the method proposed in this paper has better forecasting effect, which shows the forecasting effectiveness of this method.

AN ALGORITHMIC COMPUTATION OF CORRELATION DIMENSION FROM TIME SERIES

2007 ◽  
Vol 21 (02n03) ◽  
pp. 129-138 ◽  
Author(s):  
K. P. HARIKRISHNAN ◽  
G. AMBIKA ◽  
R. MISRA
Keyword(s):  
Time Series ◽  
Hypothesis Testing ◽  
Correlation Dimension ◽  
Visual Inspection ◽  
Chaotic Systems ◽  
Synthetic Data ◽  
Data Sets ◽  
Data Points ◽  
Scaling Region ◽  
Low Dimensional

We present an algorithmic scheme to compute the correlation dimension D2 of a time series, without requiring the visual inspection of the scaling region in the correlation sum. It is based on the standard Grassberger–Proccacia [GP] algorithm for computing D2. The scheme is tested using synthetic data sets from several standard chaotic systems as well as by adding noise to low-dimensional chaotic data. We show that the scheme is efficient with a few thousand data points and is most suitable when a nonsubjective comparison of D2 values of two time series is required, such as, in hypothesis testing.

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