{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T04:05:20Z","timestamp":1748750720830,"version":"3.41.0"},"publisher-location":"Cham","reference-count":11,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319250397"},{"type":"electronic","value":"9783319250403"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-25040-3_24","type":"book-chapter","created":{"date-parts":[[2015,10,24]],"date-time":"2015-10-24T21:45:20Z","timestamp":1445723120000},"page":"213-221","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hessian Structures and Non-invariant (F,\u00a0G)-Geometry on a Deformed Exponential Family"],"prefix":"10.1007","author":[{"given":"K. V.","family":"Harsha","sequence":"first","affiliation":[]},{"given":"K. S. Subrahamanian","family":"Moosath","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,4,3]]},"reference":[{"key":"24_CR1","series-title":"Translations of Mathematical Monographs","volume-title":"Methods of Information Geometry","author":"SI Amari","year":"2000","unstructured":"Amari, S.I., Nagaoka, H.: Methods of Information Geometry. Translations of Mathematical Monographs. Oxford University Press, Oxford (2000)"},{"issue":"5","key":"24_CR2","doi-asserted-by":"publisher","first-page":"2472","DOI":"10.3390\/e16052472","volume":"16","author":"KV Harsha","year":"2014","unstructured":"Harsha, K.V., Subrahamanian Moosath, K.S.: $$F$$ -geometry and Amari\u2019s $$\\alpha $$ -geometry on a statistical manifold. Entropy 16(5), 2472\u20132487 (2014)","journal-title":"Entropy"},{"key":"24_CR3","unstructured":"Naudts, J.: Estimators, escort probabilities, and phi-exponential families in statistical physics. J. Ineq. Pure Appl. Math., 5(4) (2004). Article no 102"},{"key":"24_CR4","doi-asserted-by":"publisher","first-page":"3552","DOI":"10.3390\/e16073552","volume":"16","author":"S Eguchi","year":"2014","unstructured":"Eguchi, S., Komori, O., Ohara, A.: Duality of maximum entropy and minimum divergence. Entropy 16, 3552\u20133572 (2014)","journal-title":"Entropy"},{"key":"24_CR5","doi-asserted-by":"publisher","first-page":"4308","DOI":"10.1016\/j.physa.2012.04.016","volume":"391","author":"SI Amari","year":"2012","unstructured":"Amari, S.I., Ohara, A., Matsuzoe, H.: Geometry of deformed exponential families: invariant, dually flat and conformal geometries. Phys. A Stat. Mech. Appl. 391, 4308\u20134319 (2012)","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"24_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/978-3-642-40020-9_29","volume-title":"Geometric Science of Information","author":"H Matsuzoe","year":"2013","unstructured":"Matsuzoe, H., Henmi, M.: Hessian structures on deformed exponential families. In: Nielsen, F., Barbaresco, F. (eds.) GSI 2013. LNCS, vol. 8085, pp. 275\u2013282. Springer, Heidelberg (2013)"},{"key":"24_CR7","doi-asserted-by":"publisher","first-page":"1170","DOI":"10.3390\/e13061170","volume":"13","author":"SI Amari","year":"2011","unstructured":"Amari, S.I., Ohara, A.: Geometry of q-exponential family of probability distributions. Entropy 13, 1170\u20131185 (2011)","journal-title":"Entropy"},{"key":"24_CR8","unstructured":"Matsuzoe, H. and Ohara, A. : Geometry for $$q-$$ exponential families. In: Proceedings of the 2nd International Colloquium on Differential Geometry and its Related Fields, Veliko Tarnovo, 6\u201310 September (2010)"},{"key":"24_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/978-3-642-15381-5_19","volume-title":"Intelligent Data Engineering and Automated Learning \u2013 IDEAL 2010","author":"Y Fujimoto","year":"2010","unstructured":"Fujimoto, Y., Murata, N.: A generalization of independence in naive bayes model. In: Fyfe, C., Tino, P., Charles, D., Garcia-Osorio, C., Yin, H. (eds.) IDEAL 2010. LNCS, vol. 6283, pp. 153\u2013161. Springer, Heidelberg (2010)"},{"key":"24_CR10","doi-asserted-by":"crossref","unstructured":"Harsha, K.V., Subrahamanian Moosath, K.S.: Geometry of $$F$$ -likelihood Estimators and $$F$$ -Max-Ent Theorem. In: AIP Conference Proceedings Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2014), Amboise, France, 21\u201326 September 2014, vol. 1641, pp. 263\u2013270 (2015)","DOI":"10.1063\/1.4905987"},{"key":"24_CR11","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1016\/j.physa.2015.03.023","volume":"433","author":"KV Harsha","year":"2015","unstructured":"Harsha, K.V., Subrahamanian Moosath, K.S.: Dually flat geometries of the deformed exponential family. Phys. A 433, 136\u2013147 (2015)","journal-title":"Phys. A"}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-25040-3_24","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,31]],"date-time":"2025-05-31T03:53:24Z","timestamp":1748663604000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-25040-3_24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319250397","9783319250403"],"references-count":11,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-25040-3_24","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"3 April 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}