Time Series Research for Neuroscience

In working on my research agenda and research grants for UOP, I return to my thoughts while at WVU in the development of spatial-temporal models for neuroscientific research. So far, the work on this blog has examined algorithmic trading with time series methods and these techniques can easily be extending to modeling electrical brain activity. Thus, one does not shift gears by looking at the human brain as an investment portfolio that contains different financial instruments sold in different spatial markets. Real-time is "real-time" and thus one architecture can easily apply to the other if you understand the essence, i.e. a Plato reference.

For example, recent developments in the use of both spatial and time series methods for modeling the measurements from MEG/EEG data have become important. By nature, time series methods are confined to the temporal domain, but in this context they apply to the spatial domain as well. For example, electro-magnetic changes are measures at between 20 to 100 different locations on the brain’s surface at every ten milliseconds. Another example, using functional MRI (fMRI) data which generates over 140,000 dimensional time series every 2-3 seconds, requires spatial-temporal modeling as well. Because of the complexity in both spatial and temporal domains, the neuroscientific community is expected to build models that both describe and understand this complexity. Here is the overlap between building data trading models for the stock market at different frequencies and modeling the brain.

Examples of computational neuroscience software for time series data can be found at (http://home.earthlink.net/~perlewitz/sftwr.html#timeseries) and comes in a wide variety of flavors. However, I like the approach mentioned in my last Blog entry by Kratzig on building user-interface frameworks such as in Java that accommodate implementation of the latest advances in research by using the API of statistical engines. Furthermore, the use of different model ontologies developed in Protégé and Owl, i.e. models, parameters, algorithms, statistics, diagnostics that can be shared would lead to great progress in the area. Ultimately, instead of all possible models being estimated, analyzed and deployed, spatial time series characteristics can suggest different models in the form of an expert system to provide real-time analysis and prediction. Microsoft’s SQL Server 2008 now provides a spatial engine to combine with its temporal data types that can aid in this type of pattern recognition.

Current methods being used such as ICA (Independent Component Analysis) and SPM (Statistical Parametric Mapping) have become popular techniques, but ignore the stochastic dynamics inherent in the time series. Of course, developments in both spatial statistics and the used of improved probability models with both frequency and Bayesian approaches in modeling the higher movements, i.e. conditional means, variances, skewness and kurtosis lead to models with more realistic dynamics that can show meaningful cross-correlations, co-integrations and emergent phenomenon, i.e. chaos theory. Furthermore, the use of wavelet techniques to decompose the time series among different spatial channels provide additional opportunities to gain valuable insight into both the frequencies, harmonics and their correlations in both the spatial and temporal domains.

My current and ongoing research is four-fold

(1) Understanding of the different model types presented in the literature for spatial temporal modeling in both the frequency and Bayesian paradigms available to the neuroscientist

(2) The development and deployment in different languages of the statistical algorithms for (1)

(3) The construction of software, i.e. APIs for different statistical engines that implement both (1) and (2) in the context of solving and describing neuro-scientific problems as mentioned above

(4) Description of ways to move (1)-(3) into expert systems to aid in the accurate diagnosis of pathologies for training fellow neuroscientists

All four parts of this research agenda fits the Boyer model through discovery, teaching, integration, and application. Ultimately, architectures are ontologies as well and there will come a time when these will automatically generate code to solve particular problems without any human intervention. Meanwhile, experimentation is needed to distill these rules...But I digress.

The reference list below is just a small sample of the developing literature in this regard.

References

Galka, A. Yamashita, O. Ozaki, T. (2004) "GARCH modelling of covariance in dynamical estimation of inverse solutions", Physics Letters A, 333, 261-268.

Jimenez,J.C., Ozaki,T.,(2005)"An approximate innovation method for the estimation of diffusion processes from discrete data", J. Time Series Analysis, in press.

Riera, J., Aubert,E., Iwata, K., Kawashima R., Wan,X., Ozaki, T.,(2005)"Fusing EEG and fMRI
based on a bottom-up model: inferring activation and effective connectivity in neural masses"Phul. Trans. of Royal Society, Biological Sciences, vol.360, no.1457, 1025-1041.

Riera, J., Yamashita,O., Kawashima, R., Sadato,N., Okada,T., Ozaki,T.(2004) "fMRI activation maps based on the NN-ARX model", Neuroimage, 23, 680-697.

Wong, K.F., Galka, A., Yamashita, O and, Ozaki, T.,(2005) "Modelling non-stationary variance in EEG time series by state space GARCH model",Computers in Biology and Medicine, in press.

Yamashita,O., Sadato,N., Okada,T. and Ozaki, T.,(2005) "Evaluating frequency-wise directed connectivity of BOLD signals applyinhg relative power contribution with the linear multivariate time series models", Neuroimage, vol.25, 478-490.

Yamashita,O., Galka,A., Ozaki,T., Biscay,R. and Valdes-Sosa,P.(2004) "Recursive least squares solution for dynamic inverse problems of EEG generation", Human Brain Mapping, Vol.21, Issue 4, 221-235.