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Statistical analysis of coupled time series with Kernel Cross-Spectral Density operators

Michel Besserve, Nikos K. Logothetis, Bernhard Schölkopf
2013 Neural Information Processing Systems  
To achieve this goal, we study the properties of the Kernel Cross-Spectral Density (KCSD) operator induced by positive definite kernels on arbitrary input domains.  ...  Here we provide a general framework for the statistical analysis of these dependencies when random variables are sampled from stationary time-series of arbitrary objects.  ...  We therefore refer to this object as the Kernel Cross-Spectral Density operator (KCSD).  ... 
dblp:conf/nips/BesserveLS13 fatcat:awedh6sjffhene7zrucoejaa5i

Methodology and Convergence Rates for Functional Time Series Regression

Tung Pham, Victor Panaretos
2018 Statistica sinica  
We consider a general framework of potentially nonlinear processes, expoiting recent advances in the spectral analysis of functional time series.  ...  to estimate the spectral density operator at a nonparametric rate, as opposed to the parametric rate for covariance operator estimation.  ...  These can be smoothed using W (T ) , in order to yield the estimators of the spectral density operator of X (and spectral density kernel), and of the cross-spectral density operator of (X, Y ), F XX ω,  ... 
doi:10.5705/ss.202016.0536 fatcat:lzubngndmvf5poddilm5bz5rwy

Functional Lagged Regression with Sparse Noisy Observations [article]

Tomáš Rubín, Victor M. Panaretos
2020 arXiv   pre-print
The spectral density of the regressor time series and the cross-spectral density between the regressors and response time series are estimated by kernel smoothing methods from the sparse observations.  ...  A functional (lagged) time series regression model involves the regression of scalar response time series on a time series of regressors that consists of a sequence of random functions.  ...  Likewise we denote the (cross)-spectral density kernel and the (cross)-spectral density operator as f * ω and F * ω .  ... 
arXiv:1905.07218v2 fatcat:iucdjv2sxzb2xd53crplkhucpq

Comparison of correlation analysis techniques for irregularly sampled time series

K. Rehfeld, N. Marwan, J. Heitzig, J. Kurths
2011 Nonlinear Processes in Geophysics  
We find a 40 % lower RMSE for the lag-1 autocorrelation function (ACF) for the Gaussian kernel method vs. the linear interpolation scheme,in the analysis of highly irregular time series.  ...  </strong> Geoscientific measurements often provide time series with irregular time sampling, requiring either data reconstruction (interpolation) or sophisticated methods to handle irregular sampling.  ...  Software to analyze irregularly sampled time series using the methods in this paper can be found on Acknowledgements.  ... 
doi:10.5194/npg-18-389-2011 fatcat:mfndjhctorh75ffkfv3ehkigai

Granger causality revisited

Karl J. Friston, André M. Bastos, Ashwini Oswal, Bernadette van Wijk, Craig Richter, Vladimir Litvak
2014 NeuroImage  
in terms of cross-spectral density, cross-covariance, autoregressive coefficients and directed transfer functions.  ...  This technical paper offers a critical re-evaluation of (spectral) Granger causality measures in the analysis of biological timeseries.  ...  These simulations are accessed through the graphical user interface of the Neural_demo Toolbox ('Granger causality').  ... 
doi:10.1016/j.neuroimage.2014.06.062 pmid:25003817 pmcid:PMC4176655 fatcat:52ufa4rjyrchlfap23v7knkvm4

The labile brain. I. Neuronal transients and nonlinear coupling

K. J. Friston
2000 Philosophical Transactions of the Royal Society of London. Biological Sciences  
This paper deals with some basic aspects of neuronal dynamics, interactions, coupling and implicit neuronal codes.  ...  The distinction between linear and nonlinear coupling has fundamental implications for the analysis and characterization of neuronal interactions, most of which are predicated on linear (synchronous) coupling  ...  In conclusion, using an analysis of the statistical dependence between spectral densities measured at di¡erent points in the brain, the existence of asynchronous coupling can be readily con¢rmed.  ... 
doi:10.1098/rstb.2000.0560 pmid:10724457 pmcid:PMC1692735 fatcat:zgbkqldr5zgcxcv4jfylkkgw3u

Two photon amplitude of partially coherent partially entangled electromagnetic fields [article]

Miguel Angel Olvera, Sonja Franke-Arnold
2015 arXiv   pre-print
By using the generalised Siegert relations and the coherent mode representation of the cross spectral density matrix the two photon amplitude is fully characterised for partially coherent beams.  ...  In this paper the underpinning theory of two photon amplitude functions for down-converted fields with partially coherent pump beams is investigated.  ...  In section 3 the cross spectral density operator is introduced. The expected value of this operator is related to the two photon amplitude trough the kernel of the one photon amplitude.  ... 
arXiv:1507.08623v1 fatcat:kwyy3haij5d2vgqgfw5ibwspgi

Nonparametric Spectral Analysis of Multivariate Time Series

Rainer von Sachs
2019 Annual Review of Statistics and Its Application  
Spectral analysis of multivariate time series has been an active field of methodological and applied statistics for the past 50 years.  ...  In this work, we give a nonexhaustive review of the mostly recent nonparametric methods of spectral analysis of multivariate time series, with an emphasis on model-based approaches.  ...  INTRODUCTION Spectral analysis of multivariate time series has been an active field of methodological and applied statistics for the past 50 years.  ... 
doi:10.1146/annurev-statistics-031219-041138 fatcat:rkhudga6zvbxtfyqc7ify4hjya

Estimation of Time-Varying Coherence and Its Application in Understanding Brain Functional Connectivity

Cheng Liu, William Gaetz, Hongmei Zhu
2010 EURASIP Journal on Advances in Signal Processing  
We show that the intimate connection between the Cohen's class-based spectra and the evolutionary spectra defined on the locally stationary time series can be linked by the kernel functions of the Cohen's  ...  The Stockwell measures can be studied in the framework of the Cohen's class distributions with a generalized frequency-dependent kernel function.  ...  Acknowledgments The authors would like to thank the financial support from Natural Sciences and Engineering Research Council of Canada and Ontario Centres of Excellence.  ... 
doi:10.1155/2010/390910 fatcat:c47ycs3zq5dvfh76nei7ck7ley

Inferring directionality of coupled dynamical systems using Gaussian process priors: Application on neurovascular systems

Ameer Ghouse, Luca Faes, Gaetano Valenza
2021 Physical review. E  
In spite of its success in the literature, the presence of process noise raises concern about CCM's ability to uncover coupling direction.  ...  Dynamical system theory has recently shown promise for uncovering causality and directionality in complex systems, particularly using the method of convergent cross mapping (CCM).  ...  Ministry of Education and Research (MIUR) in the framework of the CrossLab project (Departments of Excellence).  ... 
doi:10.1103/physreve.104.064208 pmid:35030953 fatcat:inprjmy2xzbtrfaku7vjwnyt6e

The measure of randomness by leave-one-out prediction error in the analysis of EEG after laser painful stimulation in healthy subjects and migraine patients

2005 Clinical Neurophysiology  
and controls, by the use of a novel analysis, based upon a parametric approach to measure predictability of short and noisy time series.  ...  An analysis time of 1 s after the stimulus was submitted to a time-frequency analysis by a complex Morlet wavelet and to a crosscorrelation analysis, in order to detect the development of EEG changes and  ...  Power spectral density As an indicator of the spectral power in beta band we evaluated the power spectral density using the Welch method.  ... 
doi:10.1016/j.clinph.2005.08.019 pmid:16253556 fatcat:mtsaorsbonbtfmnff3abzn7f7u

A DCM for resting state fMRI

Karl J. Friston, Joshua Kahan, Bharat Biswal, Adeel Razi
2014 NeuroImage  
This technical note introduces a dynamic causal model (DCM) for resting state fMRI time series based upon observed functional connectivity-as measured by the cross spectra among different brain regions  ...  This DCM is based upon a deterministic model that generates predicted crossed spectra from a biophysically plausible model of coupled neuronal fluctuations in a distributed neuronal network or graph.  ...  This is because the cross covariance and spectral density functions between two time series are antisymmetric.  ... 
doi:10.1016/j.neuroimage.2013.12.009 pmid:24345387 pmcid:PMC4073651 fatcat:nftnds5uifbare552z3vm4yzge

A new nonlinear similarity measure for multichannel signals

Jian-Wu Xu, Hovagim Bakardjian, Andrzej Cichocki, Jose C. Principe
2008 Neural Networks  
Cross-correntropy nonlinearly maps the original time series into a high-dimensional reproducing kernel Hilbert space (RKHS).  ...  We propose a novel similarity measure, called the correntropy coefficient, sensitive to higher order moments of the signal statistics based on a similarity function called the cross-correntopy.  ...  Acknowledgments This work was partially supported by NSF grant ECS-0601271, Graduate Alumni Fellowship from University of Florida and research scholarship from RIKEN Brain Science Institute.  ... 
doi:10.1016/j.neunet.2007.12.039 pmid:18272331 fatcat:stofkpoivrh6fijy7qccqqozxq

Mutual Information in Frequency and Its Application to Measure Cross-Frequency Coupling in Epilepsy

Rakesh Malladi, Don H. Johnson, Giridhar P. Kalamangalam, Nitin Tandon, Behnaam Aazhang
2018 IEEE Transactions on Signal Processing  
The inferred cross-frequency coupling characteristics are essential to optimize the spatial and spectral parameters of electrical stimulation based treatments of epilepsy.  ...  We then describe two data-driven estimators of MI-in-frequency: one based on kernel density estimation and the other based on the nearest neighbor algorithm and validate their performance on simulated  ...  Karunakaran for the helpful discussions on statistical hypothesis testing and proofreading the manuscript.  ... 
doi:10.1109/tsp.2018.2821627 fatcat:6iclj2xgs5at7mruemofywcofy

Generalized Convolution Spectral Mixture for Multitask Gaussian Processes

Kai Chen, Twan van Laarhoven, Perry Groot, Jinsong Chen, Elena Marchiori
2020 IEEE Transactions on Neural Networks and Learning Systems  
We focus on spectral mixture (SM) kernels and propose an enhancement of this type of kernels, called multitask generalized convolution SM (MT-GCSM) kernel.  ...  Each task in MT-GCSM has its GCSM kernel with its number of convolution structures, and dependencies between all components from different tasks are considered.  ...  A SM kernel, here denoted by K SM , is derived through modeling a spectral density (Fourier transform of a kernel) with Gaussian mixtures.  ... 
doi:10.1109/tnnls.2020.2980779 pmid:32305940 fatcat:pin44oa6vjh5ffg4st5lxzimpm
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