{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T15:49:29Z","timestamp":1740152969457,"version":"3.37.3"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,9,7]],"date-time":"2019-09-07T00:00:00Z","timestamp":1567814400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,9,7]],"date-time":"2019-09-07T00:00:00Z","timestamp":1567814400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100002241","name":"Japan Science and Technology Agency","doi-asserted-by":"crossref","award":["JPMJCR1402"],"award-info":[{"award-number":["JPMJCR1402"]}],"id":[{"id":"10.13039\/501100002241","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["18H03303","18K11459"],"award-info":[{"award-number":["18H03303","18K11459"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Rev Socionetwork Strat"],"published-print":{"date-parts":[[2019,10]]},"DOI":"10.1007\/s12626-019-00053-1","type":"journal-article","created":{"date-parts":[[2019,9,7]],"date-time":"2019-09-07T07:02:45Z","timestamp":1567839765000},"page":"281-306","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Sublinear Computational Time Modeling by Momentum-Space Renormalization Group Theory in Statistical Machine Learning Procedures"],"prefix":"10.1007","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9630-2748","authenticated-orcid":false,"given":"Kazuyuki","family":"Tanaka","sequence":"first","affiliation":[]},{"given":"Masayuki","family":"Ohzeki","sequence":"additional","affiliation":[]},{"given":"Muneki","family":"Yasuda","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,7]]},"reference":[{"key":"53_CR1","volume-title":"Probabilistic graphical models: Principles and techniques","author":"D Koller","year":"2009","unstructured":"Koller, D., & Friedman, N. (2009). Probabilistic graphical models: Principles and techniques. New York: MIT Press."},{"key":"53_CR2","volume-title":"Machine learning: A probabilistic perspective","author":"KP Murphy","year":"2012","unstructured":"Murphy, K. P. (2012). Machine learning: A probabilistic perspective. New York: MIT Press."},{"key":"53_CR3","unstructured":"Opper, M., & Saad, D. (Eds.). (2001). Advanced Mean Field Methods \u2013 Theory and Practice \u2013. MIT Press."},{"issue":"37","key":"53_CR4","doi-asserted-by":"publisher","first-page":"R81","DOI":"10.1088\/0305-4470\/35\/37\/201","volume":"35","author":"K Tanaka","year":"2002","unstructured":"Tanaka, K. (2002). Statistical\u2013mechanical approach to image processing. Journal of Physics A Mathematical and General, 35(37), R81\u2013R150.","journal-title":"Journal of Physics A Mathematical and General"},{"issue":"7","key":"53_CR5","doi-asserted-by":"publisher","first-page":"2282","DOI":"10.1109\/TIT.2005.850085","volume":"51","author":"JS Yedidia","year":"2005","unstructured":"Yedidia, J. S., Freeman, W. T., & Weiss, Y. (2005). Constructing free-energy approximations and generalized belief propagation algorithms. IEEE Transactions on Information Theory, 51(7), 2282\u20132312.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"33","key":"53_CR6","doi-asserted-by":"publisher","first-page":"R309","DOI":"10.1088\/0305-4470\/38\/33\/R01","volume":"38","author":"A Pelizzola","year":"2005","unstructured":"Pelizzola, A. (2005). Cluster variation method in statistical physics and probabilistic graphical models. Journal of Physics A Mathematical and General, 38(33), R309\u2013R339. (Topical Review).","journal-title":"Journal of Physics A Mathematical and General"},{"key":"53_CR7","unstructured":"Wainwright, M. J., & Jordan, M. I. (2008). Graphical Models, Exponential Families, and Variational Inference. : now Publishing Inc."},{"key":"53_CR8","unstructured":"M\u00e9zard, M., & Montanari, A. (2009). Information. New York, USA: Physics and Computation Oxford University Press."},{"issue":"2","key":"53_CR9","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/0370-1573(74)90023-4","volume":"12","author":"KG Wilson","year":"1974","unstructured":"Wilson, K. G., & Kogut, J. (1974). The renormalization group and the $${\\epsilon }$$ expansion. Physics Report (Section C of Physics Letters), 12(2), 75\u2013200.","journal-title":"Physics Report (Section C of Physics Letters)"},{"issue":"4","key":"53_CR10","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1103\/RevModPhys.46.597","volume":"46","author":"ME Fisher","year":"1974","unstructured":"Fisher, M. E. (1974). The renormalization group in the theory of critical behavior. Review of Modern Physics, 46(4), 597\u2013616.","journal-title":"Review of Modern Physics"},{"issue":"9","key":"53_CR11","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1103\/RevModPhys.55.583","volume":"55","author":"KG Wilson","year":"1983","unstructured":"Wilson, K. G. (1983). The renormalization group and critical phenomena. Review of Modern Physics, 55(9), 583\u2013600.","journal-title":"Review of Modern Physics"},{"key":"53_CR12","doi-asserted-by":"publisher","DOI":"10.1142\/5715","volume-title":"Field theory, the renormalization group, and critical phenomena: Graphs to computers","author":"DJ Amit","year":"2005","unstructured":"Amit, D. J., & Martin-Mayor, V. (2005). Field theory, the renormalization group, and critical phenomena: Graphs to computers. Singapore: World Scientific."},{"key":"53_CR13","volume-title":"Elements of phase transitions and critical phenomena","author":"H Nishimori","year":"2011","unstructured":"Nishimori, H., & Ortiz, G. (2011). Elements of phase transitions and critical phenomena. Oxford: Oxford University Press."},{"issue":"4","key":"53_CR14","doi-asserted-by":"publisher","first-page":"Article ID: 045","DOI":"10.7566\/JPSJ.84.045001","volume":"84","author":"K Tanaka","year":"2015","unstructured":"Tanaka, K., Kataoka, S., Yasuda, M., & Ohzeki, M. (2015). Inverse renormalization group transformation in Bayesian image segmentations. Journal of the Physical Society of Japan, 84(4), Article ID: 045001.","journal-title":"Journal of the Physical Society of Japan"},{"issue":"8","key":"53_CR15","doi-asserted-by":"publisher","first-page":"Article ID: 085","DOI":"10.7566\/JPSJ.87.085001","volume":"87","author":"K Tanaka","year":"2018","unstructured":"Tanaka, K., Nakamura, M., Kataoka, S., Ohzeki, M., & Yasuda, M. (2018). Momentum-space renormalization group transformation in Bayesian image modeling by Gaussian graphical model. Journal of the Physical Society of Japan, 87(8), Article ID: 085001.","journal-title":"Journal of the Physical Society of Japan"},{"issue":"1","key":"53_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"AP Dempster","year":"1977","unstructured":"Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society Series B (Methodological), 39(1), 1\u201338. (with discussions).","journal-title":"Journal of the Royal Statistical Society Series B (Methodological)"},{"key":"53_CR17","doi-asserted-by":"publisher","DOI":"10.1002\/9781119995678","volume-title":"Mixtures: Estimation and applications","author":"KL Mengersen","year":"2011","unstructured":"Mengersen, K. L., Robert, C. P., & Titterington, D. M. (2011). Mixtures: Estimation and applications. Oxford: Wiley."},{"key":"53_CR18","series-title":"Lecture notes in mathematics","first-page":"113","volume-title":"Random fields and inverse problems in imaging","author":"D Geman","year":"1990","unstructured":"Geman, D. (1990). Random fields and inverse problems in imaging (Vol. 1427, pp. 113\u2013193)., Lecture notes in mathematics Berlin: Springer."},{"key":"53_CR19","doi-asserted-by":"publisher","DOI":"10.1201\/9780203492024","volume-title":"Gaussian Markov random fields: Theory and applications","author":"H Rue","year":"2005","unstructured":"Rue, H., & Held, L. (2005). Gaussian Markov random fields: Theory and applications. Boca Raton: CRC."},{"issue":"37","key":"53_CR20","doi-asserted-by":"publisher","first-page":"11285","DOI":"10.1088\/1751-8113\/40\/37\/007","volume":"40","author":"K Tanaka","year":"2007","unstructured":"Tanaka, K., & Titterington, D. M. (2007). Statistical trajectory of approximate EM algorithm for probabilistic image processing. Journal of Physics A Mathematical and Theoretical, 40(37), 11285\u201311300.","journal-title":"Journal of Physics A Mathematical and Theoretical"},{"issue":"2","key":"53_CR21","doi-asserted-by":"publisher","first-page":"Article ID.0250","DOI":"10.1143\/JPSJ.81.025001","volume":"81","author":"S Kataoka","year":"2012","unstructured":"Kataoka, S., Yasuda, M., & Tanaka, K. (2012). Statistical analysis of Gaussian image inpainting problems. Journal of the Physical Society of Japan, 81(2), Article ID.025001.","journal-title":"Journal of the Physical Society of Japan"},{"issue":"2","key":"53_CR22","doi-asserted-by":"publisher","first-page":"Article ID: 025","DOI":"10.1088\/0266-5611\/30\/2\/025003","volume":"30","author":"S Kataoka","year":"2014","unstructured":"Kataoka, S., Yasuda, M., Furtlehner, C., & Tanaka, K. (2014). Traffic data reconstruction based on Markov random field modeling. Inverse Problems, 30(2), Article ID: 025003.","journal-title":"Inverse Problems"},{"issue":"4","key":"53_CR23","doi-asserted-by":"publisher","first-page":"Article ID: 042","DOI":"10.1103\/PhysRevE.90.042137","volume":"90","author":"T Kuwatani","year":"2014","unstructured":"Kuwatani, T., Nagata, K., Okada, M., & Toriumi, M. (2014). Markov-random-field modeling for linear seismic tomography. Physical Review E, 90(4), Article ID: 042137.","journal-title":"Physical Review E"},{"key":"53_CR24","doi-asserted-by":"publisher","first-page":"Article ID: 5","DOI":"10.1186\/1880-5981-66-5","volume":"66","author":"T Kuwatani","year":"2014","unstructured":"Kuwatani, T., Nagata, K., Okada, M., & Toriumi, M. (2014). Markov random field modeling for mapping geofluid distributions from seismic velocity structures. Earth Planets and Space, 66, Article ID: 5.","journal-title":"Earth Planets and Space"},{"key":"53_CR25","volume-title":"Statistical field theory","author":"G Parisi","year":"1988","unstructured":"Parisi, G. (1988). Statistical field theory. Boston: Addison-Wesley."},{"key":"53_CR26","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511622779","volume-title":"Statistical field theory: Volume 1 from brown motion to renormalization and lattice gauge theory","author":"C Itzykson","year":"1989","unstructured":"Itzykson, C., & Drouffee, J.-M. (1989). Statistical field theory: Volume 1 from brown motion to renormalization and lattice gauge theory. Cambridge: Cambridge University Press."},{"key":"53_CR27","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511622779","volume-title":"Statistical field theory: Volume 2 strong coupling, Monte Carlo Methods, conformal field theory, and random systems","author":"C Itzykson","year":"1989","unstructured":"Itzykson, C., & Drouffee, J.-M. (1989). Statistical field theory: Volume 2 strong coupling, Monte Carlo Methods, conformal field theory, and random systems. Cambridge: Cambridge University Press."}],"container-title":["The Review of Socionetwork Strategies"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12626-019-00053-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12626-019-00053-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12626-019-00053-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,6]],"date-time":"2020-09-06T00:00:36Z","timestamp":1599350436000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12626-019-00053-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,7]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,10]]}},"alternative-id":["53"],"URL":"https:\/\/doi.org\/10.1007\/s12626-019-00053-1","relation":{},"ISSN":["2523-3173","1867-3236"],"issn-type":[{"type":"print","value":"2523-3173"},{"type":"electronic","value":"1867-3236"}],"subject":[],"published":{"date-parts":[[2019,9,7]]},"assertion":[{"value":"13 February 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 August 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 September 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}