Correcting Multivariate Auto-Regressive Models for the Influence of Unobserved Common Input

We consider the problem of inferring connectivity from timeseries data under the presence of time-dependent common input originating from non-measured variables. We analyze a simple method to filter out the influence of such confounding variables in multivariate autoregressive models (MVAR). The method learns the parameters of an extended MVAR model with latent variables. Using synthetic MVAR models we characterize where connectivity reconstruction is possible and useful and show that regularization is convenient when the common input has strong influence. We also illustrate how the method can be used to correct partial directed coherence, a causality measure used often in the neuroscience community.

[1]  Luiz A. Baccalá,et al.  Partial directed coherence: a new concept in neural structure determination , 2001, Biological Cybernetics.

[2]  R. E. Greenblatt,et al.  Connectivity measures applied to human brain electrophysiological data , 2012, Journal of Neuroscience Methods.

[3]  Motoaki Kawanabe,et al.  Modeling Sparse Connectivity Between Underlying Brain Sources for EEG/MEG , 2009, IEEE Transactions on Biomedical Engineering.

[4]  Kaare Brandt Petersen,et al.  State-Space Models: From the EM Algorithm to a Gradient Approach , 2007, Neural Computation.

[5]  Alois Schlögl,et al.  Analyzing event-related EEG data with multivariate autoregressive parameters. , 2006, Progress in brain research.

[6]  Giulio Tononi,et al.  Estimation of Cortical Connectivity From EEG Using State-Space Models , 2010, IEEE Transactions on Biomedical Engineering.

[7]  J. Schoffelen,et al.  Source connectivity analysis with MEG and EEG , 2009, Human brain mapping.

[8]  Zoubin Ghahramani,et al.  A Unifying Review of Linear Gaussian Models , 1999, Neural Computation.

[9]  Robert Oostenveld,et al.  Gain of the human dura in vivo and its effects on invasive brain signal feature detection , 2010, Journal of Neuroscience Methods.

[10]  Luca Faes,et al.  Measuring Connectivity in Linear Multivariate Processes: Definitions, Interpretation, and Practical Analysis , 2012, Comput. Math. Methods Medicine.

[11]  Tohru Katayama,et al.  Subspace Methods for System Identification , 2005 .

[12]  K. Sameshima,et al.  Connectivity Inference between Neural Structures via Partial Directed Coherence , 2007 .

[13]  Bart De Moor,et al.  N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems , 1994, Autom..

[14]  Karen O. Egiazarian,et al.  Measuring directional coupling between EEG sources , 2008, NeuroImage.

[15]  Vicenç Gómez,et al.  The Variational Garrote , 2011, Machine Learning.

[16]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .