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G. Hannak, A. Jung, N. Görtz:
"On the Information-theoretic Limits of Graphical Model Selection for Gaussian Time Series";
Talk: European Signal Processing Conference (EUSIPCO), Lissabon, Portugal; 09-01-2014 - 09-05-2014; in: "Proceedings of the European Signal Processing Conference (EUSIPCO)", (2014), 516 - 520.

We consider the problem of inferring the conditional inde- pendence graph (CIG) of a multivariate stationary dicrete- time Gaussian random process based on a finite length ob- servation. Using information-theoretic methods, we derive a lower bound on the error probability of any learning scheme for the underlying process CIG. This bound, in turn, yields a minimum required sample-size which is necessary for any algorithm regardless of its computational complexity, to reli- ably select the true underlying CIG. Furthermore, by analysis of a simple selection scheme, we show that the information- theoretic limits can be achieved for a subclass of processes having sparse CIG. We do not assume a parametric model for the observed process, but require it to have a sufficiently smooth spectral density matrix (SDM).

We consider the problem of inferring the conditional inde- pendence graph (CIG) of a multivariate stationary dicrete- time Gaussian random process based on a finite length ob- servation. Using information-theoretic methods, we derive a lower bound on the error probability of any learning scheme for the underlying process CIG. This bound, in turn, yields a minimum required sample-size which is necessary for any algorithm regardless of its computational complexity, to reli- ably select the true underlying CIG. Furthermore, by analysis of a simple selection scheme, we show that the information- theoretic limits can be achieved for a subclass of processes having sparse CIG. We do not assume a parametric model for the observed process, but require it to have a sufficiently smooth spectral density matrix (SDM).

http://publik.tuwien.ac.at/files/PubDat_231845.pdf