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Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of the unknown data generating density.
On the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums
Gerber, H. (1982) · 1982
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Nonlinear component analysis as a kernel eigenvalue problem
Schölkopf, B., Smola, A., and Müller, K.-R. (1998) · 1998
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Nonlinear dimensionality reduction by locally linear embedding
Roweis, S. and Saul, L. K. (2000) · 2000
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A global geometric framework for nonlinear dimensionality reduction
Tenenbaum, J., de Silva, V., and Langford, J. C. (2000) · 2000
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Charting a manifold
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Stochastic neighbor embedding
Hinton, G. E. and Roweis, S. (2003) · 2002
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Manifold Parzen windows
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Laplacian eigenmaps for dimensionality reduction and data representation
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Unsupervised learning of image manifolds by semidefinite programming
Weinberger, K. Q. and Saul, L. K. (2004) · 2004
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Lee, H., Grosse, R., Ranganath, R., and Ng, A. Y. (2009) · 2009
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Deep Boltzmann machines
Salakhutdinov, R. and Hinton, G. (2009) · 2009
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Sample complexity of testing the manifold hypothesis
Narayanan, H. and Mitter, S. (2010) · 2010
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The Toronto face dataset
Susskind, J., Anderson, A., and Hinton, G. E. (2010) · 2010
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Contracting auto-encoders: Explicit invariance during feature extraction
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The manifold tangent classifier
Rifai, S., Dauphin, Y., Vincent, P., Bengio, Y., and Muller, X. (2011c) · 2011
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A generative process for sampling contractive auto-encoders
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