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Abstract: In order to realize an input-output relation given by noise-contaminated examples, it is effective to use a stochastic model of neural networks. A model network includes hidden units whose activation values are not specified nor observed. It is useful to estimate the hidden variables from the observed or specified input-output data based on the stochastic model. Two algorithms, the EM - and em-algorithms, have so far been proposed for this purpose. The EM-algorithm is an iterative... (Update)
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BibTeX entry: (Update)
Amari, S. (in press) Information geometry of the EM and em algorithms for neural networks, Neural Networks. Baum, L.E., and Sell, G.R. (1968), Growth transformation for functions on manifolds, Pac. J. Math., 27, 211-227. http://citeseer.ist.psu.edu/amari95information.html More
@article{ amari95information,
author = "Shun-ichi Amari",
title = "Information Geometry of the {EM} and {em} Algorithms for Neural Networks",
journal = "Neural Networks",
volume = "8",
number = "9",
pages = "1379--1408",
year = "1995",
url = "citeseer.ist.psu.edu/amari95information.html" }
Citations (may not include all citations):2528 Maximum likelihood from incomplete data via the EM algorithm (context) - Dempster, Laird et al. - 1977
376 A learning algorithm for Boltzmann machines (context) - Ackley, Hinton et al. - 1985 ACM DBLP
303 Stochastic relaxation (context) - Geman, Geman - 1984
228 Simulated Annealing and Boltzmann Machines (context) - Aarts, Korst - 1989
223 Linear Statistical Inference and its Applications (context) - Rao - 1973
130 Spatial statistics and Bayesian computation (context) - Besag, Green - 1993
104 A new view of the EM algorithm that justifies incremental an.. - Neal, Hinton - 1993
101 Differential Geometrical Methods in Statistics (context) - Amari - 1985
73 A maximization technique occuring in the statistical analysi.. (context) - Baum, Petrie et al. - 1970
61 Theoretical Statistics (context) - Cox, Hinkley - 1974
56 divergence geometry of probability distributions and minimiz.. (context) - Csisz'ar - 1975
45 Information and Exponential Families in Statistical Theory (context) - Barndorff-Nielsen - 1978
35 Information geometry and alternating minimization procedures (context) - Csisz'ar, Tusn'ady - 1984
31 Information geometry of Boltzmann machines (context) - Amari, Kurata et al. - 1992
29 Information and accuracy attainable in the estimation of sta.. (context) - Rao - 1945
22 Differential geometry of curved exponential families --- cur.. (context) - Amari - 1982
21 Information geometry of estimating functions in semiparametr.. - Amari, Kawanabe - 1994
16 Mathematical foundations of neurocomputing (context) - Amari - 1990
15 The geometry of asymptotic inference (context) - Kass - 1989
15 Dualistic geometry of the manifold of higher-order neurons (context) - Amari - 1991 ACM
14 Alternating minimization and Boltzmann machine learning (context) - Byrne - 1992
14 The EM algorithm and information geometry in neural network .. (context) - Amari - 1994 ACM
13 Differential Geometry and Statistics (context) - Murray, Rice - 1993
11 Differential Geometry in Statistical Inferences (context) - Amari, Barndorff-Nielsen et al. - 1987
10 Identifiability of hidden Markov information sources and the.. (context) - Ito, Amari et al. - 1992
9 Differential geometry of a parametric family of invertible l.. (context) - Amari
9 Limit Theorems for large deviations (context) - Saulis, Statulevicius - 1989
7 Differential geometry of smooth families of probability dist.. (context) - Nagaoka, Amari - 1982
7 Hidden Markov random fields (context) - Gunsch, Geman et al. - 1994
7 Differential geometrical theory of statistics (context) - Amari
7 Statistical inference under multi-terminal rate restrictions.. (context) - Amari, Han - 1989
7 The role of differential geometry in statistical theory (context) - Barndorff-Nielsen, Cox et al. - 1986
6 Fisher information under restriction of Shannon information .. (context) - Amari - 1989
6 Parametric Statistical Model and Likelihood (context) - Barndorff-Nielsen - 1988
5 Asymptotic theory of sequential estimation : differential ge.. (context) - Okamoto, Amari - 1991
5 Estimation of network parameters in semiparametric stochasti.. - Kawanabe, Amari - 1994
3 Learning in artificial networks: A statistical perspective (context) - White - 1989
2 Approximating exponential models (context) - Barndorff-Nielsen, Jupp - 1989
2 A new criterion for selecting models from partially observed.. - Shimodaira - 1993
2 Dualistic dynamical systems in the framework of information .. - Fujiwara, Amari - 1994
2 Notes on Conjugate Connections (context) - Nomizu, Simon - 1991
1 Piecewise-linear division of signal space by a multilayer ne.. (context) - Zhuang, Amari - 1993
1 New gating net for mixture of experts (context) - Xu, Jordan et al. - 1994
1 Higherarchical mixtures of experts and the EM-algorithm (context) - Jordan, Jacobs - 1994
1 Neural networks and related method for clasification (context) - Ripley - 1994
1 Differential geometric structures of stable feedback systems.. (context) - Ohara, Amari - 1992
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