A multivariate phase distribution and its estimation
Oscillations have received considerable attention within the neuroscience community. Early theories of large-scale brain dynamics focused on oscillations [1], and oscillatory dynamics have recently received widespread interest [2, 3, 4]. Neural oscillations are hypothesized to be functionally involved in a wide range of tasks, such as representing sensory information, regulating the flow of information, learning and recalling of information, and binding of distributed information.
In each of these contexts, the phase of neural oscillations is of central scientific interest. For example, the pair-wise relationships of phase variables recovered from ECoG recordings (electrical potentials recorded simultaneously from a grid of 64 electrodes) show strong statistical dependencies [5]. The coupling of these oscillations may indicate common sources of input or task based cortico-cortical communication. High-dimensional neural measurements of oscillatory dynamics (such as ECoG, EEG, LFP, or fMRI) pose two interconnected problems: how do we model the full multivariate distribution of phase measurements, and how do we recover the parameters of such a model from phase measurements?
In order to address these questions, and ultimately to provide tools for the scientific investigation of neural oscillations, we have developed models and analytical techniques that can capture the observed statistical dependencies among multiple phase variables and recover the parameters of these models from measurements. In this work we introduce a distribution that captures empirically observed pair-wise phase relationships: the distribution produces uniformly distributed marginals of the individual phase variables and dependencies in the differences of pairs of phases. Importantly, we have developed a computationally efficient and accurate technique for estimating the parameters of this distribution from data using the Score Matching technique [6]. We show that the algorithm performs well in high-dimensions (d=100), and in cases with limited data (as few as 10 samples per dimension). This distribution and estimation technique can be broadly applied to any setting that produces multiple circular variables and is useful for localizing behaviorally dependent functional networks [7].
References
1. W.J. Freeman. Mass Action in the Nervous System. Academic Press, New York, 1975.
2. P. Fries. A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. Trends in Cognitive Sciences, 9(10):474-480, 2005.
3. T.J. Sejnowski and O. Paulsen. Network Oscillations: Emerging Computational Principles. Journal of Neuroscience, 26(6):1673, 2006.
4. R. Canolty and K. Miller. Large scale brain dynamics. NIPS Workshop, 2007.
5. C.F. Cadieu and K. Koepsell. A multivariate phase distribution and its estimation. arXiv:0809.4291v1 [q-bio.NC], September 2008.
6. A. Hyvarinen. Estimation of Non-Normalized Statistical Models by Score Matching. The Journal of Machine Learning Research, 6:695-709, 2005.
7. A. Huth, C.F. Cadieu, C.L. Dale, G.V. Simpson, K. Koepsell. Detecting functional connectivity in networks of phase-coupled neural oscillators. Cosyne 2009.
Conference:
Computational and systems
neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009.
Presentation Type:
Poster Presentation
Topic:
Poster Presentations
Citation:
(2009). A multivariate phase distribution and its estimation.
Front. Syst. Neurosci.
Conference Abstract:
Computational and systems
neuroscience 2009.
doi: 10.3389/conf.neuro.06.2009.03.260
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Received:
04 Feb 2009;
Published Online:
04 Feb 2009.