Local distance preservation in the GP-LVM through back constraints

By Neil D. Lawrence, Joaquin Quiñonero Candela. 2006

277 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Signal Processing

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Citations in the corpus

Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness (2020, background): “Distance-preserving neural networks and bi-Lipschitz condition The theoretic connection between distance preservation and the bi-Lipschitz condition is well-established (Searcód, 2006), and learning an approximately isometric, distancepreserving transform has been an important goal in the fields of ”
Bayesian representation learning with oracle constraints (2015, background): “e but tackle using the crowd-information as a regularizer. Constraints on latent variables models in an otherwise unsupervised setting have also found early usage in the context of Gaussian Processes [12] using backconstraints, but those differ in nature compared to the constraints we consider here.”
High-Dimensional Probability Estimation with Deep Density Models (2013, methodology): “Other approaches, such as the the back-constrained GP-LVM [Lawrence and Candela, 2006] attempt to approximate this bijection.”
Automatic model construction with Gaussian processes (2014, background): “This difficulty might be resolved by using a warping with back-constraints (Lawrence, 2006), which would allow a more direct evaluation of the density at a given point in the observed space.”
Using Deep Belief Nets to Learn Covariance Kernels for Gaussian Processes (2007, background): “3 with respect to the parameters of the covariance function using the labeled training data[9].”
Learning GP-BayesFilters via Gaussian process latent variable models (2009, background): “GPs learn probabilistic regression models from training data consisting of input-output examples (Rasmussen and Williams 2005).”
Latent spaces for dynamic movement primitives (2009, background): “Similarly, Lawrence and QuinoneroCandela [16] try to strengthen neighbourhood relations between points by constraining the mapping from data to latent space to be smooth as well.”
Foundations and Advances in Deep Learning (2014, background): “, LeCun et al., 2010). Lee et al. (2009) showed that this way of incrementally stacking convolutional layers enables the neural network, specifically a convolutional deep belief network in their work, to learn hierarchical part-based representations of data.”
Nonparametric guidance of autoencoder representations using label information (2012, methodology): “…where the k th covariance matrix Σ θ k ,φ now depends not only on the kernel hyperparameters θ k , but also on the parameters of g ( y ; φ ), i.e., Lawrence and Qui˜nonero-Candela (2006) motivate the back-constrained GPLVM partially through the NeuroScale algorithm of Lowe and Tipping (1997).”
Learning a Parametric Embedding by Preserving Local Structure (2009, unknown): “, in NeuroScale (Lowe and Tipping, 1996) and back-constrained GPLVMs (Lawrence and Candela, 2006).”
Dimension Reduction for Aerodynamic Design Optimization (2011, methodology): “Many variants of the method have been developed over recent years [45–48].”
Variational Auto-encoded Deep Gaussian Processes (2015, background): “Lawrence & Qui˜nonero Candela (2006) constrained the latent inputs of a GP with a parametric model to enforce local distance preservation in the inputs; Ek et al. (2008) followed the same approach for constraining the latent space with information from additional views of the data.”
Hybrid and ensemble-based soft computing techniques in bankruptcy prediction: a survey (2010, background): “sional data onto a low-dimensional space (Lawrence and Quinonero-Candela 2006).”
Efficient high dimensional maximum entropy modeling via symmetric partition functions (2012, unknown): “Also notable are latent variable models that employ Gaussian process regression to probabilistically represent observation models and the latent dynamics [14, 10, 7].”