Cited by 1,011Neural Networks and ApplicationsTopic ModelingImage and Signal Denoising Methods

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A Connection Between Score Matching and Denoising Autoencoders

Vincent, Pascal·2011·Neural Computation

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Abstract

Denoising autoencoders have been previously shown to be competitive alternatives to restricted Boltzmann machines for unsupervised pretraining of each layer of a deep architecture. We show that a simple denoising autoencoder training criterion is equivalent to matching the score (with respect to the data) of a specific energy-based model to that of a nonparametric Parzen density estimator of the data. This yields several useful insights. It defines a proper probabilistic model for the denoising autoencoder technique, which makes it in principle possible to sample from them or rank examples by their energy. It suggests a different way to apply score matching that is related to learning to denoise and does not require computing second derivatives. It justifies the use of tied weights between the encoder and decoder and suggests ways to extend the success of denoising autoencoders to a larger family of energy-based models.

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Advances in neural information processing systems 7
Cios, K. J., & Shields, M. E. (1997) · Neurocomputing · doi:10.1016/s0925-2312(97)90018-7 · Cited by 22,093
A fast learning algorithm for deep belief nets
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Self-citation
Extracting and composing robust features with denoising autoencoders
Vincent, P., Larochelle, H., Bengio, Y., & Manzagol, P.-A. (2008) · Proceedings of the 25th international conference on Machine learning - ICML '08 · doi:10.1145/1390156.1390294 · Cited by 7,436
Self-citation
Training Products of Experts by Minimizing Contrastive Divergence
Hinton, G. E. (2002) · Neural Computation · doi:10.1162/089976602760128018 · Cited by 4,879 · cited 3×
“1Specifically SM (Hyvärinen, 2005), minimum velocity learning (Movellan, 2008), and certain forms of contrastive divergence (Hinton, 2002; Welling & Hinton, 2002) are all recast as minimizing the Kullback-Leibler divergence between the data distribution and the distribution obtained after running, for infinitesimal ti…”
BackgroundMethod
Greedy layer-wise training of deep networks
Bengio, Y., Lamblin, P., Popovici, D., & Larochelle, H. (2007) · Advances in Neural Information Processing Systems 19 · doi:10.7551/mitpress/7503.003.0024 · Cited by 4,841
Hybrid Monte Carlo
Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987) · Physics Letters B · doi:10.1016/0370-2693(87)91197-x · Cited by 4,081
Stacked Denoising Autoencoders: Learning Useful Representations in a Deep Network with a Local Denoising Criterion
(2010) · Journal of Machine Learning Research · doi:10.5555/1756006.1953039 · Cited by 4,051
Self-citation
Why Does Unsupervised Pre-training Help Deep Learning?
Erhan, D., Bengio, Y., Courville, A. C., Manzagol, P.-A., Vincent, P., & Samy Bengio, A. (2010) · Cited by 2,180
Self-citation
Advances in Neural Information Processing Systems 18
Murray, I., Mackay, D., Zoubin Ghahramani, A., & Skilling, J. (2006) · Cited by 1,927

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Erhan D., 2010, Journal of Machine Learning Research, 11, 625
Gallinari P., 1987, Proceedings of COGNITIVA 87
Hyvärinen A., 2005, Journal of Machine Learning Research, 6, 695
Vincent P., 2010, Journal of Machine Learning Research, 11, 3371

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Authors: Vincent, P.
Affiliations: Université de Montréal (CA)
Corresponding author: Vincent, Pascal
Venue: Neural Computation
Publisher: MIT Press
Published: 2011-07
Volume: 23
Issue: 7
Pages: 1661-1674
ISSN: 0899-7667 (ISSN-L)
1530-888X
DOI: 10.1162/neco_a_00142
OpenAlex: W2013035813
Cited by: 1,011
References: 29
Citations by year: 2026: 131 · 2025: 254 · 2024: 198 · 2023: 126 · 2022: 46 · 2021: 59 · 2020: 52 · 2019: 29 · 2018: 20 · 2017: 22 · 2016: 20 · 2015: 14 · 2014: 9 · 2013: 14 · 2012: 9
FWCI: 11.49
Type: journal article
Language: en
Open access: closed
Locations: Neural Computation (publishedVersion)
PubMed (publishedVersion)
Topics: Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
Physical Sciences › Computer Science › Artificial Intelligence › Topic Modeling
Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
Keywords: score matching, denoising autoencoder, energy-based models, unsupervised pre-training, restricted Boltzmann machine, probabilistic models, deep learning architectures
MeSH terms: Computer Simulation, Models, Statistical

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A Connection Between Score Matching and Denoising Autoencoders

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