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

Besserve, M., Logothetis, N., & Schölkopf, B. (2014). Statistical analysis of coupled time series with Kernel Cross-Spectral Density operators. In C. Burges, L. Bottou, M. Welling, Z. Ghahramani, & K. Weinberger (Eds.), Advances in Neural Information Processing Systems 26 (pp. 2535-2543). Red Hook, NY, USA: Curran.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-001A-1269-2 Version Permalink: https://hdl.handle.net/21.11116/0000-0001-2D52-1
Genre: Conference Paper

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 Creators:
Besserve, M1, 2, Author           
Logothetis, NK1, 2, Author           
Schölkopf, B3, Author           
Affiliations:
1Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497798              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              
3Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society, ou_1497647              

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 Abstract: Many applications require the analysis of complex interactions between time series. These interactions can be non-linear and involve vector valued as well as complex data structures such as graphs or strings. Here we provide a general framework for the statistical analysis of these interactions when random variables are sampled from stationary time-series of arbitrary objects. To achieve this goal we analyze the properties of the kernel cross-spectral density operator induced by positive definite kernels on arbitrary input domains. This framework enables us to develop an independence test between time series as well as a similarity measure to compare different types of coupling. The performance of our test is compared to the HSIC test using i.i.d. assumptions, showing improvement in terms of detection errors as well as the suitability of this approach for testing dependency in complex dynamical systems. Finally, we use this approach to characterize complex interactions in electrophysiological neural time series.

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 Dates: 2013-122014
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: BesserveLS2013
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Title: Twenty-Seventh Annual Conference on Neural Information Processing Systems (NIPS 2013)
Place of Event: Lake Tahoe, NV, USA
Start-/End Date: -

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Title: Advances in Neural Information Processing Systems 26
Source Genre: Proceedings
 Creator(s):
Burges, CJC, Editor
Bottou, L., Editor
Welling, M., Editor
Ghahramani, Z., Editor
Weinberger, K.Q., Editor
Affiliations:
-
Publ. Info: Red Hook, NY, USA : Curran
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 2535 - 2543 Identifier: -