--- abstract: 'The discrimination technique for estimating the parameters of Gaussian mixtures that is based on the Extended Baum transformations (EB) has had significant impact on the speech recognition community. The proof that definitively shows that these transformations increase the value of an objective function with iteration (i.e., so-called "growth transformations") was presented by the author two years ago for a diagonal Gaussian mixture densities. In this paper this proof is extended to a multidimensional multivariate Gaussian mixtures. The proof presented in the current paper is based on the linearization process and the explicit growth estimate for linear forms of Gaussian mixtures. ' altloc: - 'http://domino.watson.ibm.com/library/cyberdig.nsf/1e4115aea78b6e7c85256b360066f0d4/f579eeb6173e04a8852570310063a2d7?OpenDocument&Highlight=0,speech' chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ creators_id: [] creators_name: - family: Kanevsky given: Dimitri honourific: Dr lineage: '' date: 2005-06 date_type: published datestamp: 2006-08-08 department: Human Language Technologies dir: disk0/00/00/50/58 edit_lock_since: ~ edit_lock_until: ~ edit_lock_user: ~ editors_id: [] editors_name: [] eprint_status: archive eprintid: 5058 fileinfo: /style/images/fileicons/application_pdf.png;/5058/1/rc23645.pdf full_text_status: public importid: ~ institution: IBM isbn: ~ ispublished: unpub issn: ~ item_issues_comment: [] item_issues_count: 0 item_issues_description: [] item_issues_id: [] item_issues_reported_by: [] item_issues_resolved_by: [] item_issues_status: [] item_issues_timestamp: [] item_issues_type: [] keywords: 'Multidimensional Multivariate Gaussuan Mixture, Extended Baum-Welch transformations, discriminative training, estimation of statistical parameters, maximum mutual informaiton estimation' lastmod: 2011-03-11 08:56:34 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: ~ pagerange: ~ pubdom: TRUE publication: ~ publisher: ~ refereed: FALSE referencetext: |-2 S. Axelrod, V. Goel, R. Gopinath, P. Olsen, and K. Visweswariah, "Discriminative Training of Subspace Constrained GMMs for Speech Recognition," to be submitted to IEEE Transactions on Speech and Audio Processing. L.E.Baum and J.A. Eagon, "An inequality with applications to statistical prediction for functions of Markov processes and to a model of ecology," Bull. Amer. Math. Soc., vol. 73, pp.360-363, 1967. A. Gunawardana and W. Byrne, ``Discriminative Speaker Adaptation with Conditional Maximum Likelihood Linear Regression,'' ICASSP, 2002. P.S. Gopalakrishnan, D. Kanevsky, D. Nahamoo and A. Nadas, "An inequality for rational functions with applications to some statistical estimation problems", IEEE Trans. Information Theory, Vol. 37, No.1 January 1991 D. Kanevsky, "Growth Transformations for General Functions", RC22919 (W0309-163), September 25, 2003. D. Kanevsky, "Extended Baum transformations for general functions", in Proc. ICASSP, 2004. Y. Normandin, "An improved MMIE Training Algorithm for Speaker Independent, Small Vocabulary, Continuous Speech Recognition", Proc. ICASSP'91, pp. 537-540, 1991. R. Schluter, W. Macherey, B. Muler and H. Ney, "Comparison of discriminative training criteria and optimization methods for speech recognition", Speech Communication, Vol. 34, pp.287-310, 2001. V. Valtchev , P.C. Woodland and S. J. Young, "Lattice-based Discriminative Training for Large Vocabulary Speech Recognition Systems", Speech Communication, Vol. 22, pp. 303-314, 1996. relation_type: [] relation_uri: [] reportno: RC23645(W0506-120) rev_number: 12 series: ~ source: ~ status_changed: 2007-09-12 17:06:45 subjects: - comp-sci-stat-model succeeds: ~ suggestions: ~ sword_depositor: ~ sword_slug: ~ thesistype: ~ title: 'EXTENDED BAUM TRANSFORMATIONS FOR GENERAL FUNCTIONS, II' type: techreport userid: 6589 volume: ~