{"_id":"ZPYr6Jwmzd8Spfu8K","bibbaseid":"hannak-jung-goertz-ontheinformationtheoreticlimitsofgraphicalmodelselectionforgaussiantimeseries-2014","authorIDs":[],"author_short":["Hannak, G.","Jung, A.","Goertz, N."],"bibdata":{"bibtype":"inproceedings","type":"inproceedings","author":[{"firstnames":["G."],"propositions":[],"lastnames":["Hannak"],"suffixes":[]},{"firstnames":["A."],"propositions":[],"lastnames":["Jung"],"suffixes":[]},{"firstnames":["N."],"propositions":[],"lastnames":["Goertz"],"suffixes":[]}],"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","bibtex":"@InProceedings{6952142,\n author = {G. Hannak and A. Jung and N. Goertz},\n booktitle = {2014 22nd European Signal Processing Conference (EUSIPCO)},\n title = {On the information-theoretic limits of graphical model selection for Gaussian time series},\n year = {2014},\n pages = {516-520},\n 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).},\n 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},\n issn = {2076-1465},\n month = {Sep.},\n url = {https://www.eurasip.org/proceedings/eusipco/eusipco2014/html/papers/1569924169.pdf},\n}\n\n","author_short":["Hannak, G.","Jung, A.","Goertz, N."],"key":"6952142","id":"6952142","bibbaseid":"hannak-jung-goertz-ontheinformationtheoreticlimitsofgraphicalmodelselectionforgaussiantimeseries-2014","role":"author","urls":{"Paper":"https://www.eurasip.org/proceedings/eusipco/eusipco2014/html/papers/1569924169.pdf"},"keyword":["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"],"metadata":{"authorlinks":{}}},"bibtype":"inproceedings","biburl":"https://raw.githubusercontent.com/Roznn/EUSIPCO/main/eusipco2014url.bib","creationDate":"2021-02-13T17:43:41.617Z","downloads":0,"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"],"search_terms":["information","theoretic","limits","graphical","model","selection","gaussian","time","series","hannak","jung","goertz"],"title":"On the information-theoretic limits of graphical model selection for Gaussian time series","year":2014,"dataSources":["A2ezyFL6GG6na7bbs","oZFG3eQZPXnykPgnE"]}