Citation Relationships
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Ikeda S, Tanaka T, Amari S (2004) Stochastic reasoning, free energy, and information geometry. Neural Comput 16:1779-810 [PubMed]
References and models cited by this paper | References and models that cite this paper | |
Amari S (1998) Natural gradient works efficiently in learning Neural Comput 10:251-276 Amari S (2001) Information geometry on hierarchical decomposition of stochastic interactions IEEE Transaction On Information Theory 47:1701-1711 Amari S, Ikeda S, Shimokawa H (2001) Information geometry and meanfield approximation: The Œ+ projection approach Advanced mean field methods: Theory and practive, Opper M:Saad D, ed. pp.241 Amari S, Nagaoka H (2000) Methods of information geometry Drouffe C (1989) Statistical field theory Heskes T (2003) Stable fixed points of loopy belief propagation are minima of the Bethe free energy Advances in neural information processing systems, Becker S:Thrun S:Obermayer K, ed. pp.359 Ikeda S, Tanaka T, Amari S (2002) Information geometrical framework for analyzing belief propagation decoder Advances in neural information processing systems, Dietterich T:Becker S:Ghahramani Z, ed. pp.407 Ikeda S, Tanaka T, Amari S (2004) Information geometry of turbo codes and low-density parity-check codes IEEE Trans Inform Theory Jordan MI, Ghahramani Z, Jaakkola TS, Saul LK (1998) Learning in graphical models Kabashima Y, Saad D (1999) Statistical mechanics of error-correcting codes Europhysics Lett 45:97-103 Kabashima Y, Saad D (2001) The TAP approach to intensive and extensive connectivity systems Advanced mean field methods: Theory and practice, Opper M:Saad D, ed. pp.65 Lauritzen S, Spiegelhalter D (1988) Local computations with probabilities on graphical structures and their application to expert systems J Royal Stat Soc Series B 50:157-224 Pearl J (1988) Probabilistic reasoning in intelligent systems Press WH, Teukolsky SA, Vellerling WT, Flannery BP (1992) Numerical Recipes In C: The Art Of Scientific Computing Richardson T (2000) The geometry of turbo-decoding dynamics IEEE Trans Inform Theory 46:9-23 Tanaka T (2000) Information geometry of mean-field approximation. Neural Comput 12:1951-68 [PubMed] Tanaka T (2001) Information geometry of mean-field approximation Advanced mean field methods: Theory and practice, Opper M:Saad D, ed. pp.259 Wainwright M, Jaakkola T, Willsky A (2002) Tree-based reparameterization for approximate inference on loopy graphs Advances in neural information processing systems, Dietterich TG:Becker S:Ghahramani Z, ed. pp.1001 Wainwright M, Jaakkola T, Willsky A (2003) Tree-reweighted belief propagation algorithms and approximate ML estimate by pseudo-moment matching Proc 9th Intl Workshop Artificial Intelligence and Statistics, Available on-line at:http:--wwwfiresearch.microsoft.com-conferences-aistats2003-, Bishop CM:Frey BJ, ed. Weiss Y (2000) Correctness of local probability in graphical models with loops. Neural Comput 12:1-41 [PubMed] Yedidia J, Freeman W, Weiss Y (2000) Generalized belief propagation Advances in neural information processing systems, Leen t:Dietterich T:Tresp V, ed. pp.689 Yedidia J, Freeman W, Weiss Y (2001) Bethe free energy, Kikuchi approximations, and belief propagation algorithms Tech. Rep. TR2001-16 Yuille AL (2002) CCCP algorithms to minimize the Bethe and Kikuchi free energies: convergent alternatives to belief propagation. Neural Comput 14:1691-722 [Journal] [PubMed] Yuille AL, Rangarajan A (2003) The concave-convex procedure. Neural Comput 15:915-36 [Journal] [PubMed] | Amari S (2007) Integration of stochastic models by minimizing alpha-divergence. Neural Comput 19:2780-96 [Journal] [PubMed] | |