%0 Book Section %1 statphys23_0132 %A Tanaka, K. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K advanced computer field inference learning mean method probabilistic quantum science spin statistical statphys23 system topic-11 %T Advanced mean field methods in quantum probabilistic inference %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=132 %X Recently, some statistical-mechanical methods have been applied to problems in computer sciences1. Particularly, it has been known that the mean field theory is one of powerful one also for computer sciences. On the other hand, some physisists have started to be interested in the application of quantum spin systems2-4. In the present talk, we formulate probabilistic inference systems by means of Bayesian statistics and quantum spin systems on any graph consisting of nodes and links. Algorithms for the practical applications are constructed by using advanced mean field methods, particularly, Bethe approximation and cluster variation method for quantum spin systems. The present talk is placed as one of fundamental studies for applications of statistical mechanics to computer sciences. Quantum spin systems for probabilistic inferences are defined on graphs with nodes and links. For such spin systems, Bethe approximation is one of useful methods. However, many probabilistic inference systems often include some multi-body interactions and we need cluster variation method to construct approximate algorithms for them. The author has been published some investigations in the advanced mean field method with the linear response theory for conventional probabilistic inferences5. The present talk is one of the extensions of the previous papers for conventional probabilistic inferences to the advanced mean field method in probabilistic inferences formulated by means of reduced density matrices including some quantum fields. enumerate ıtem H. Nishimori: Statistical Physics of Spin Glasses and Information Processing, ---An Introduction--- (Oxford University Press, 2001). ıtem K. Tanaka: Statistical-mechanical approach to image processing (Topical Review), J. Phys. A: Math. Gen., 35, pp.R81-R150 (2002). ıtem H. Nishimori and P. Sollich: Error counting in a quantum error-correcting code and the ground-state energy of a spin glass, J. Phys. Soc. Jpn. 73, 2701 (2004). ıtem S. Morita and H. Nihimori: Convergence theorems for quantum annealing, J. Phys. A, 39, 13903 (2006). ıtem K. Tanaka: Probabilistic inference by means of cluster variation method and linear response theory, IEICE Transactions on Information and Systems, E86-D, 1228 (2003). enumerate

@incollection{statphys23_0132, abstract = {Recently, some statistical-mechanical methods have been applied to problems in computer sciences[1]. Particularly, it has been known that the mean field theory is one of powerful one also for computer sciences. On the other hand, some physisists have started to be interested in the application of quantum spin systems[2-4]. In the present talk, we formulate probabilistic inference systems by means of Bayesian statistics and quantum spin systems on any graph consisting of nodes and links. Algorithms for the practical applications are constructed by using advanced mean field methods, particularly, Bethe approximation and cluster variation method for quantum spin systems. The present talk is placed as one of fundamental studies for applications of statistical mechanics to computer sciences. Quantum spin systems for probabilistic inferences are defined on graphs with nodes and links. For such spin systems, Bethe approximation is one of useful methods. However, many probabilistic inference systems often include some multi-body interactions and we need cluster variation method to construct approximate algorithms for them. The author has been published some investigations in the advanced mean field method with the linear response theory for conventional probabilistic inferences[5]. The present talk is one of the extensions of the previous papers for conventional probabilistic inferences to the advanced mean field method in probabilistic inferences formulated by means of reduced density matrices including some quantum fields. \begin{enumerate} \item{} H. Nishimori: Statistical Physics of Spin Glasses and Information Processing, ---An Introduction--- (Oxford University Press, 2001). \item{} K. Tanaka: Statistical-mechanical approach to image processing (Topical Review), J. Phys. A: Math. Gen., {\bf 35}, pp.R81-R150 (2002). \item{} H. Nishimori and P. Sollich: Error counting in a quantum error-correcting code and the ground-state energy of a spin glass, J. Phys. Soc. Jpn. {\bf 73}, 2701 (2004). \item{} S. Morita and H. Nihimori: Convergence theorems for quantum annealing, J. Phys. A, {\bf 39}, 13903 (2006). \item{} K. Tanaka: Probabilistic inference by means of cluster variation method and linear response theory, IEICE Transactions on Information and Systems, {\bf E86-D}, 1228 (2003). \end{enumerate}}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Tanaka, K.}, biburl = {https://www.bibsonomy.org/bibtex/2f326b5d4424af407544608d4bd836fdf/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {26558eaff6bf3beb38d246961af79c53}, intrahash = {f326b5d4424af407544608d4bd836fdf}, keywords = {advanced computer field inference learning mean method probabilistic quantum science spin statistical statphys23 system topic-11}, month = {9-13 July}, timestamp = {2007-06-20T10:16:12.000+0200}, title = {Advanced mean field methods in quantum probabilistic inference}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=132}, year = 2007 }