On the information-theoretic limits of graphical model selection for Gaussian time series. Hannak, G., Jung, A., & Goertz, N. In *2014 22nd European Signal Processing Conference (EUSIPCO)*, pages 516-520, Sep., 2014.

Paper abstract bibtex

Paper abstract bibtex

We consider the problem of inferring the conditional independence graph (CIG) of a multivariate stationary dicrete-time Gaussian random process based on a finite length observation. 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 reliably 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).

@InProceedings{6952142, author = {G. Hannak and A. Jung and N. Goertz}, booktitle = {2014 22nd European Signal Processing Conference (EUSIPCO)}, title = {On the information-theoretic limits of graphical model selection for Gaussian time series}, year = {2014}, pages = {516-520}, abstract = {We consider the problem of inferring the conditional independence graph (CIG) of a multivariate stationary dicrete-time Gaussian random process based on a finite length observation. 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 reliably 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).}, keywords = {computational complexity;Gaussian processes;graph theory;information theory;matrix algebra;time series;information-theoretic limits;graphical model selection;Gaussian time series;conditional independence graph;CIG;multivariate stationary dicrete-time Gaussian random process;finite length observation;error probability;learning scheme;computational complexity;smooth spectral density matrix;SDM;Graphical models;Time series analysis;Covariance matrices;Reliability;Vectors;Indexes;Correlation;CIG;Fano-inequality;stationary time series}, issn = {2076-1465}, month = {Sep.}, url = {https://www.eurasip.org/proceedings/eusipco/eusipco2014/html/papers/1569924169.pdf}, }

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