Non-Local Manifold Parzen Windows

By Yoshua Bengio, Hugo Larochelle, Pascal Vincent. 2005

65 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

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In Probabilistic & Bayesian Methods

Citations in the corpus

Generalized Denoising Auto-Encoders as Generative Models (2013, background): “This idea is already behind the non-local manifold Parzen windows (Bengio et al. , 2006a) and non-local manifold tangent learning (Bengio et al. , 2006b) algorithms: the local density around a point ˜ X can be approximated by a multivariate Gaussian whose covariance matrix has leading eigenvectors…”
A Generative Process for Contractive Auto-Encoders (2012, methodology): “A ﬁrst non-linear manifold learning algorithm with non-local generalization was proposed by Bengio et al. (2006a), stimulating the work presented here, which also follows up on more recent work in the area of Deep Learning (Hinton et al., 2006; Bengio, 2009), more speciﬁcally the Con-tractive…”
Representation Learning: A Review and New Perspectives (2012, background): “The nearest neighbor graph is simply not sufficiently densely populated to map out satisfyingly the wrinkles of the target manifold [17], [22], [16].”
Learning Structured Embeddings of Knowledge Bases (2011, background): “…is appealing for several reasons: it is flexible (simple to adapt to many KBs), compact (only a low-dimension vector per entity and a low-dimension matrix per relation type to store) and also exhibits generalization ability (the ability to infer new relations from the existing ones in the KB).”
Deep Learning of Representations: Looking Forward (2013, methodology): “In comparison, Bengio et al. (2013a) report a log-likelihood of -244 for RBMs, using the same setting.”
Unsupervised Feature Learning and Deep Learning: A Review and New Perspectives (2012, methodology): “In early work in this direction (Bengio et al., 2006b), a parametrized function fθ (an MLP) was trained to predict the tangent space associated to any given point x.”
A review of novelty detection (2014, methodology): “[87] describe a non-local non-parametric density estimator which builds upon previously proposed GMMs with regularised covariance matrices to take into account the local shape of the manifold.”
Higher Order Contractive Auto-Encoder (2011, background): “Non-local manifold Parzen windows [3] learns a function to explicitly output tangent directions at a point, whereas the CAE’s tangent directions are to be found in the Jacobian matrix of the mapping function it learns.”
How Auto-Encoders Could Provide Credit Assignment in Deep Networks via Target Propagation (2014, methodology): “In order to avoid adding noise in unwanted directions that would yield poor generated samples, two possibilities arise, which can be combined: • Make the Parzen model more sophisticated, making it more concentrated in some directions, e.g., using a local covariance estimator at each location, as wit”
Wireless Networks Design in the Era of Deep Learning: Model-Based, AI-Based, or Both? (2019, background): “This has been shown to enable deep learning to generalize non-locally [102].”
Static and space-time visual saliency detection by self-resemblance. (2009, methodology): “an isotropic kernel is not the most appropriate tool [ 2 ], [4] , [39].”
The Manifold Tangent Classifier (2011, background): “One attempt to generalize the manifold shape non-locally (Bengio et al., 2006) is based on explicitly predicting the tangent plane associated to any given point x, as a parametrized function of x. Note that these algorithms all explicitly exploit training set neighborhoods (see Figure 2), i.e. they…”
Deep Learning for Event-Driven Stock Prediction (2015, background): “In theory, embeddings are appropriate for achieving good results with a density estimator (e.g. convolutional neural network), which can misbehave in high dimensions [Bengio et al., 2005].”
Nonlocal Estimation of Manifold Structure (2006, methodology): “In (Bengio and Larochelle, 2006),”