{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T13:31:03Z","timestamp":1765546263536,"version":"3.40.3"},"publisher-location":"Cham","reference-count":37,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319712482"},{"type":"electronic","value":"9783319712499"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-71249-9_20","type":"book-chapter","created":{"date-parts":[[2017,12,29]],"date-time":"2017-12-29T08:53:43Z","timestamp":1514537623000},"page":"323-338","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Entropic Trace Estimates for Log Determinants"],"prefix":"10.1007","author":[{"given":"Jack","family":"Fitzsimons","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Diego","family":"Granziol","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kurt","family":"Cutajar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Osborne","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maurizio","family":"Filippone","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen","family":"Roberts","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,12,30]]},"reference":[{"issue":"18","key":"20_CR1","doi-asserted-by":"publisher","first-page":"690","DOI":"10.1016\/j.ipl.2013.06.005","volume":"113","author":"MJ Atallah","year":"2013","unstructured":"Atallah, M.J., Grigorescu, E., Wu, Y.: A lower-variance randomized algorithm for approximate string matching. Inf. Process. Lett. 113(18), 690\u2013692 (2013)","journal-title":"Inf. Process. Lett."},{"issue":"2","key":"20_CR2","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s11222-012-9368-y","volume":"24","author":"E Aune","year":"2014","unstructured":"Aune, E., Simpson, D.P., Eidsvik, J.: Parameter estimation in high dimensional Gaussian distributions. Stat. Comput. 24(2), 247\u2013263 (2014)","journal-title":"Stat. Comput."},{"key":"20_CR3","unstructured":"Avron, H.: Counting triangles in large graphs using randomized matrix trace estimation. In: Workshop on Large-Scale Data Mining: Theory and Applications, vol. 10, pp. 10\u20139 (2010)"},{"issue":"2","key":"20_CR4","doi-asserted-by":"publisher","first-page":"8:1","DOI":"10.1145\/1944345.1944349","volume":"58","author":"H Avron","year":"2011","unstructured":"Avron, H., Toledo, S.: Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix. J. ACM (JACM) 58(2), 8:1\u20138:34 (2011)","journal-title":"J. ACM (JACM)"},{"key":"20_CR5","first-page":"29","volume":"4","author":"Z Bai","year":"1997","unstructured":"Bai, Z., Golub, G.H.: Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices. Ann. Numer. Math. 4, 29\u201338 (1997)","journal-title":"Ann. Numer. Math."},{"issue":"5","key":"20_CR6","doi-asserted-by":"publisher","first-page":"057701","DOI":"10.1103\/PhysRevE.71.057701","volume":"71","author":"K Bandyopadhyay","year":"2005","unstructured":"Bandyopadhyay, K., Bhattacharya, A.K., Biswas, P., Drabold, D.: Maximum entropy and the problem of moments: a stable algorithm. Phys. Rev. E 71(5), 057701 (2005)","journal-title":"Phys. Rev. E"},{"key":"20_CR7","unstructured":"Boutsidis, C., Drineas, P., Kambadur, P., Zouzias, A.: A randomized algorithm for approximating the log determinant of a symmetric positive definite matrix. CoRR abs\/1503.00374 (2015)"},{"issue":"01","key":"20_CR8","doi-asserted-by":"publisher","first-page":"143","DOI":"10.2307\/2331391","volume":"31","author":"PW Buchen","year":"1996","unstructured":"Buchen, P.W., Kelly, M.: The maximum entropy distribution of an asset inferred from option prices. J. Financ. Quant. Anal. 31(01), 143\u2013159 (1996)","journal-title":"J. Financ. Quant. Anal."},{"key":"20_CR9","unstructured":"Caticha, A.: Entropic Inference and the Foundations of Physics (monograph commissioned by the 11th Brazilian Meeting on Bayesian Statistics-EBEB-2012) (2012)"},{"issue":"1","key":"20_CR10","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1137\/090778250","volume":"33","author":"J Chen","year":"2011","unstructured":"Chen, J., Anitescu, M., Saad, Y.: Computing f(A)b via least squares polynomial approximations. SIAM J. Sci. Comput. 33(1), 195\u2013222 (2011)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"20_CR11","first-page":"1","volume":"38","author":"TA Davis","year":"2011","unstructured":"Davis, T.A., Hu, Y.: The University of Florida sparse matrix collection. ACM Trans. Math. Softw. (TOMS) 38(1), 1 (2011)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"20_CR12","unstructured":"Fitzsimons, J., Cutajar, K., Osborne, M., Roberts, S., Filippone, M.: Bayesian inference of log determinants (2017)"},{"key":"20_CR13","unstructured":"Fitzsimons, J., Osborne, M., Roberts, S., Fitzsimons, J.: Improved stochastic trace estimation using mutually unbiased bases. arXiv preprint arXiv:1608.00117 (2016)"},{"issue":"3","key":"20_CR14","first-page":"749","volume":"7","author":"S Gershgorin","year":"1931","unstructured":"Gershgorin, S.: Uber die Abgrenzung der Eigenwerte einer matrix. Izvestija Akademii Nauk SSSR Serija Matematika 7(3), 749\u2013754 (1931)","journal-title":"Izvestija Akademii Nauk SSSR Serija Matematika"},{"key":"20_CR15","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.physa.2016.02.069","volume":"455","author":"A Giffin","year":"2016","unstructured":"Giffin, A., Cafaro, C., Ali, S.A.: Application of the maximum relative entropy method to the physics of ferromagnetic materials. Phys. A: Stat. Mech. Appl. 455, 11\u201326 (2016). http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0378437116002478","journal-title":"Phys. A: Stat. Mech. Appl."},{"key":"20_CR16","volume-title":"Matrix Computations","author":"GH Golub","year":"1996","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)","edition":"3"},{"issue":"9","key":"20_CR17","doi-asserted-by":"publisher","first-page":"923","DOI":"10.1007\/s10701-014-9819-8","volume":"44","author":"D Gonz\u00e1lez","year":"2014","unstructured":"Gonz\u00e1lez, D., Davis, S., Guti\u00e9rrez, G.: Newtonian dynamics from the principle of maximum caliber. Found. Phys. 44(9), 923\u2013931 (2014)","journal-title":"Found. Phys."},{"key":"20_CR18","unstructured":"Granziol, D., Roberts, S.: An information and field theoretic approach to the grand canonical ensemble (2017)"},{"key":"20_CR19","unstructured":"Guinness, J., Ipsen, I.C.F.: Efficient computation of Gaussian likelihoods for stationary Markov random fields (2015)"},{"key":"20_CR20","unstructured":"Han, I., Malioutov, D., Shin, J.: Large-scale log-determinant computation through stochastic Chebyshev expansions. In: Bach, F.R., Blei, D.M. (eds.) Proceedings of the 32nd International Conference on Machine Learning, ICML 2015, Lille, France, 6\u201311 July 2015"},{"issue":"2","key":"20_CR21","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1080\/03610919008812866","volume":"19","author":"M Hutchinson","year":"1990","unstructured":"Hutchinson, M.: A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines. Commun. Stat. - Simul. Comput. 19(2), 433\u2013450 (1990)","journal-title":"Commun. Stat. - Simul. Comput."},{"key":"20_CR22","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1103\/PhysRev.106.620","volume":"106","author":"ET Jaynes","year":"1957","unstructured":"Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. 106, 620\u2013630 (1957). http:\/\/link.aps.org\/doi\/10.1103\/PhysRev.106.620","journal-title":"Phys. Rev."},{"issue":"4","key":"20_CR23","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1111\/j.1467-9868.2011.00777.x","volume":"73","author":"F Lindgren","year":"2011","unstructured":"Lindgren, F., Rue, H., Lindstr\u00f6m, J.: An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. J. Roy. Stat. Soc.: Ser. B (Stat. Methodol.) 73(4), 423\u2013498 (2011)","journal-title":"J. Roy. Stat. Soc.: Ser. B (Stat. Methodol.)"},{"key":"20_CR24","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1017\/S0001867800040313","volume":"7","author":"O Macchi","year":"1975","unstructured":"Macchi, O.: The coincidence approach to stochastic point processes. Adv. Appl. Probab. 7, 83\u2013122 (1975)","journal-title":"Adv. Appl. Probab."},{"key":"20_CR25","doi-asserted-by":"publisher","first-page":"e103","DOI":"10.7717\/peerj-cs.103","volume":"3","author":"A Meurer","year":"2017","unstructured":"Meurer, A., Smith, C.P., Paprocki, M., \u010cert\u00edk, O., Kirpichev, S.B., Rocklin, M., Kumar, A., Ivanov, S., Moore, J.K., Singh, S., Rathnayake, T., Vig, S., Granger, B.E., Muller, R.P., Bonazzi, F., Gupta, H., Vats, S., Johansson, F., Pedregosa, F., Curry, M.J., Terrel, A.R., Rou\u010dka, \u0160., Saboo, A., Fernando, I., Kulal, S., Cimrman, R., Scopatz, A.: SymPy: symbolic computing in Python. PeerJ Comput. Sci. 3, e103 (2017). https:\/\/doi.org\/10.7717\/peerj-cs.103","journal-title":"PeerJ Comput. Sci."},{"key":"20_CR26","series-title":"Fundamental Theories of Physics (An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application)","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/978-94-017-2219-3_16","volume-title":"Maximum Entropy and Bayesian Methods","author":"A Mohammad-Djafari","year":"1992","unstructured":"Mohammad-Djafari, A.: A Matlab program to calculate the maximum entropy distributions. In: Smith, C.R., Erickson, G.J., Neudorfer, P.O. (eds.) Maximum Entropy and Bayesian Methods. FTPH, vol. 50, pp. 221\u2013233. Springer, Dordrecht (1992). https:\/\/doi.org\/10.1007\/978-94-017-2219-3_16"},{"issue":"2","key":"20_CR27","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/s00780-011-0167-7","volume":"16","author":"C Neri","year":"2012","unstructured":"Neri, C., Schneider, L.: Maximum entropy distributions inferred from option portfolios on an asset. Finan. Stochast. 16(2), 293\u2013318 (2012)","journal-title":"Finan. Stochast."},{"key":"20_CR28","doi-asserted-by":"crossref","unstructured":"Nielsen, M.A., Chuang, I.: Quantum computation and quantum information (2002)","DOI":"10.1119\/1.1463744"},{"key":"20_CR29","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/0378-3758(91)90002-V","volume":"29","author":"A O\u2019Hagan","year":"1991","unstructured":"O\u2019Hagan, A.: Bayes-Hermite quadrature. J. Stat. Plan. Infer. 29, 245\u2013260 (1991)","journal-title":"J. Stat. Plan. Infer."},{"key":"20_CR30","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1103\/RevModPhys.85.1115","volume":"85","author":"S Press\u00e9","year":"2013","unstructured":"Press\u00e9, S., Ghosh, K., Lee, J., Dill, K.A.: Principles of maximum entropy and maximum caliber in statistical physics. Rev. Mod. Phys. 85, 1115\u20131141 (2013). http:\/\/link.aps.org\/doi\/10.1103\/RevModPhys.85.1115","journal-title":"Rev. Mod. Phys."},{"key":"20_CR31","volume-title":"Gaussian Processes for Machine Learning","author":"CE Rasmussen","year":"2006","unstructured":"Rasmussen, C.E., Williams, C.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)"},{"key":"20_CR32","doi-asserted-by":"crossref","DOI":"10.1201\/9780203492024","volume-title":"Gaussian Markov Random Fields: Theory and Applications, Monographs on Statistics and Applied Probability","author":"H Rue","year":"2005","unstructured":"Rue, H., Held, L.: Gaussian Markov Random Fields: Theory and Applications, Monographs on Statistics and Applied Probability, vol. 104. Chapman & Hall, London (2005)"},{"key":"20_CR33","unstructured":"Saat\u00e7i, Y.: Scalable inference for structured Gaussian process models. Ph.D. thesis, University of Cambridge (2011)"},{"issue":"1","key":"20_CR34","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1109\/TIT.1980.1056144","volume":"26","author":"J Shore","year":"1980","unstructured":"Shore, J., Johnson, R.: Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy. IEEE Trans. Inf. Theory 26(1), 26\u201337 (1980)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"20_CR35","doi-asserted-by":"crossref","unstructured":"Ubaru, S., Chen, J., Saad, Y.: Fast estimation of tr(F(A)) via stochastic Lanczos quadrature (2016)","DOI":"10.1137\/16M1104974"},{"issue":"6\u20131","key":"20_CR36","doi-asserted-by":"publisher","first-page":"2099","DOI":"10.1109\/TSP.2006.874409","volume":"54","author":"MJ Wainwright","year":"2006","unstructured":"Wainwright, M.J., Jordan, M.I.: Log-determinant relaxation for approximate inference in discrete Markov random fields. IEEE Trans. Signal Process. 54(6\u20131), 2099\u20132109 (2006)","journal-title":"IEEE Trans. Signal Process."},{"key":"20_CR37","unstructured":"Wolfram Research Inc.: Mathematica. https:\/\/www.wolfram.com\/mathematica\/"}],"container-title":["Lecture Notes in Computer Science","Machine Learning and Knowledge Discovery in Databases"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-71249-9_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T01:27:48Z","timestamp":1672277268000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-71249-9_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319712482","9783319712499"],"references-count":37,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-71249-9_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]},"assertion":[{"value":"30 December 2017","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ECML PKDD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Joint European Conference on Machine Learning and Knowledge Discovery in Databases","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Skopje","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Macedonia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2017","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 September 2017","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 September 2017","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ecml2017","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/ecmlpkdd2017.ijs.si\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}