A Localization Approach to Improve Iterative Proportional Scaling in Gaussian Graphical Models

References

• Badsberg , J. H. , Malvestuto , F. M. ( 2001 ). An implementation of the iterative proportional fitting procecure by propagation trees . Comput. Stat. Data. Anal. 37 : 297 – 322 .
   Web of Science ®Google Scholar
• Cox , D. R. , Wermuth , N. ( 1996 ). Multivariate Dependencies . London : Chapman and Hall .
   Google Scholar
• Csiszár , I. ( 1975 ). I-divergence geometry of probability distributions and minimization problems . Ann. Probab. 3 : 146 – 158 .
   Web of Science ®Google Scholar
• Dahl , J. , Vandenberghe , L. , Roychowdhury , V. ( 2008 ). Covariance selection for nonchordal graphs via chordal embedding . Optim. Meth. Software 23 : 510 – 520 .
   Google Scholar
• Deming , W. E. , Stephan , F. F. ( 1940 ). On a least squares adjustment of a sampled frequency table when the expected marginal totals are known . Ann. Math. Stat. 11 : 427 – 444 .
   Google Scholar
• Dempster , A. P. ( 1972 ). Covariance selection . Biometrics 28 : 157 – 175 .
   Web of Science ®Google Scholar
• Dirac , G. A. ( 1961 ). On rigid circuit graphs . Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 25 : 71 – 76 .
   Google Scholar
• Dobra , A. , Hans , C. , Jones , B. , Nevins , J. R. , Yao , G. , West , M. ( 2004 ). Sparse graphical models for exploring gene expression data . J. Multivariate Anal. 90 : 196 – 212 .
   Web of Science ®Google Scholar
• Drton , M. , Richardson , T. S. ( 2008 ). Graphical methods for efficient likelihood inference in Gaussian covariance models . Machine Learning Research 9 : 893 – 914 .
   Web of Science ®Google Scholar
• Edwards , D. M. ( 2000 ). Introduction to Graphical Modelling . New York : Springer .
   Google Scholar
• Fienberg , S. E. ( 1970 ). An iterative procedure for estimation in contingency tables . Ann. Math. Stat. 41 : 907 – 917 .
   Google Scholar
• Fukuda , M. , Kojima , H. , Murota , K. , Nakata , K. ( 2000 ). Exploiting sparcity in semidefinite programming via matrix completion I: General framework . SIAM J. Optim. 11 : 647 – 674 .
   Web of Science ®Google Scholar
• Ireland , C. T. , Kulback , S. ( 1968 ). Contingency table with given marginal . Biometrika 55 : 179 – 188 .
   PubMed Web of Science ®Google Scholar
• Jiroušek , R. ( 1991 ). Solution of the marginal problem and decomposable solutions . Kybernetika 27 : 403 – 412 .
   Web of Science ®Google Scholar
• Jiroušek , R. , Přeučil , S. ( 1995 ). On the effective implementation of the iterative proportional fitting procedure . Comput. Stat. Data. Anal. 19 : 177 – 189 .
   Web of Science ®Google Scholar
• Lauritzen , S. L. ( 1996 ). Graphical Models . Oxford : Oxford University Press .
   Google Scholar
• Leimer , H. G. ( 1993 ). Optimal decomposition by clique separators . Discrete Math. 113 : 99 – 123 .
   Web of Science ®Google Scholar
• Li , H. , Gui , J. ( 2006 ). Gradient directed regularization for sparse Gaussian concentration graphs, with applications to inference of genetic network . Biostatistics 7 : 302 – 317 .
   PubMed Web of Science ®Google Scholar
• Malvestuto , F. M. , Moscarini , M. (2000). Decomposition of a hypergraph by partial-edge separators. Theor. Comput. Sci. 237:57–79.
   Google Scholar
• Rose , J. D. ( 1971 ). A graph theoretic study of the numerical solution of sparse positive definite . In: Read , R. C. , ed. Graph Theory and Computing . New York : Academic Press , pp. 183 – 217 .
   Google Scholar
• Speed , T. P. , Kiiveri , H. T. ( 1986 ). Gaussian Markov distribution over finite graphs . Ann. Stat. 14 : 138 – 150 .
   Web of Science ®Google Scholar
• Whittaker , J. ( 1990 ). Graphical Models in Applied Multivariate Statistics . Chichester : John Wiley and Sons .
   Google Scholar