Isolated effective coherence (iCoh): causal information flow excluding indirect paths

A problem of great interest in real world systems, where multiple time series measurements are available, is the estimation of the intra-system causal relations. For instance, electric cortical signals are used for studying functional connectivity between brain areas, their directionality, the direct or indirect nature of the connections, and the spectral characteristics (e.g. which oscillations are preferentially transmitted). The earliest spectral measure of causality was Akaike's (1968) seminal work on the noise contribution ratio, reflecting direct and indirect connections. Later, a major breakthrough was the partial directed coherence of Baccala and Sameshima (2001) for direct connections. The simple aim of this study consists of two parts: (1) To expose a major problem with the partial directed coherence, where it is shown that it is affected by irrelevant connections to such an extent that it can misrepresent the frequency response, thus defeating the main purpose for which the measure was developed, and (2) To provide a solution to this problem, namely the "isolated effective coherence", which consists of estimating the partial coherence under a multivariate auto-regressive model, followed by setting all irrelevant associations to zero, other than the particular directional association of interest. Simple, realistic, toy examples illustrate the severity of the problem with the partial directed coherence, and the solution achieved by the isolated effective coherence. For the sake of reproducible research, the software code implementing the methods discussed here (using lazarus free-pascal "www.lazarus.freepascal.org"), including the test data as text files, are freely available at: https://sites.google.com/site/pascualmarqui/home/icoh-isolated-effective-coherenceComment: 2014-02-21 pre-print, technical report, KEY Institute for Brain-Mind Research, University of Zurich, et a

Support vector regression for functional data in multivariate calibration problems

Quantitative analyses involving instrumental signals, such as chromatograms, NIR, and MIR spectra have successfully applied nowadays for the solution of important chemical tasks. Multivariate calibration is very useful for such purposes and the commonly used methods in chemometrics consider each sample spectrum as a sequence of discrete data points. An alternative way to analyze spectral data is to consider each sample as a function, in which a functional data is obtained. Concerning regression, some linear and nonparametric regression methods have been generalized to functional data. This paper proposes the use of the recently introduced method, support vector regression for functional data (FDA-SVR) for the solution of linear and nonlinear multivariate calibration problems. Three different spectral datasets were analyzed and a comparative study was carried out to test its performance with respect to some traditional calibration methods used in chemometrics such as PLS, SVR and LS-SVR. The satisfactory results obtained with FDA-SVR suggest that it can be an effective and promising toot for multivariate calibration tasks. (C) 2008 Elsevier B.V. All rights reserved.6424167111011