The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
Information geometry of the EM and em algorithms for neural networks
Open accessAbstract
Abstract To realize an input-output relation given by noise-contaminated examples, it is effective to use a stochastic model of neural networks. When the 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 statistical technique of using the conditional expectation, and the em algorithm is a geometrical one given by information geometry. The em algorithm minimizes iteratively the Kullback-Leibler divergence in the manifold of neural networks. These two algorithms are equivalent in most cases. The present paper gives a unified information geometrical framework for studying stochastic models of neural networks, by focusing on the EM and em algorithms, and proves a condition that guarantees their equivalence. Examples include: (1) stochastic multilayer perceptron, (2) mixtures of experts, and (3) normal mixture model.
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Cites
A learning algorithm for Boltzmann machines
Ackley, D. H., Hinton, G. E., & Sejnowski, T. J. (1985) · Cognitive Science · doi:10.1207/s15516709cog0901_7 · Cited by 3,402
Differential-Geometrical Methods in Statistics
Amari, S.-I. (1985) · Lecture Notes in Statistics · doi:10.1007/978-1-4612-5056-2 · Cited by 1,673
$I$-Divergence Geometry of Probability Distributions and Minimization Problems
Csiszar, I. (1975) · The Annals of Probability · doi:10.1214/aop/1176996454 · Cited by 1,645
Enhanced MLP performance and fault tolerance resulting from synaptic weight noise during training
Murray, A. F., & Edwards, P. J. (1994) · IEEE Transactions on Neural Networks · doi:10.1109/72.317730 · Cited by 201
Cited by
The EM Algorithm—an Old Folk-song Sung to a Fast New Tune
Meng, X.-L., & Van Dyk, D. (1997) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00082 · Cited by 802
Csiszár’s Divergences for Non-negative Matrix Factorization: Family of New Algorithms
Cichocki, A., Zdunek, R., & Amari, S.-I. (2006) · Lecture Notes in Computer Science · doi:10.1007/11679363_5 · Cited by 271
Self-citationSpectral Entropies as Information-Theoretic Tools for Complex Network Comparison
De Domenico, M., & Biamonte, J. (2016) · Physical Review X · doi:10.1103/physrevx.6.041062 · Cited by 160
Towards a neuronal gauge theory
Sengupta, B., Tozzi, A., Cooray, G. K., Douglas, P. K., & Friston, K. J. (2016) · PLOS Biology · doi:10.1371/journal.pbio.1002400 · Cited by 132
Predictive Coding: a Theoretical and Experimental Review
Millidge, B., Seth, A., & Buckley, C. L. (2021) · arXiv · doi:10.48550/arxiv.2107.12979 · Cited by 106
Metadata
- Authors
- Amari, S.-I.
- Venue
- Neural Networks
- Publisher
- Elsevier BV
- Published
- 1995
- Volume
- 8
- Issue
- 9
- Pages
- 1379-1408
- ISSN
- 0893-6080 (ISSN-L)
- OpenAlex
- W2036632921
- Cited by
- 331
- References
- 4
- FWCI
- 11.49
- Type
- journal article
- Language
- en
- Open access
- green
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