Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models

By Neil D. Lawrence. 2005

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Citations in the corpus

The Variational Gaussian Process (2015, methodology): “Finally, given data x , we use stochastic optimization to ﬁnd the variational parameters that minimize the KL divergence to the model posterior.”
Stochastic Back-propagation and Variational Inference in Deep Latent Gaussian Models (2014, methodology): “The Gaussian process latent variable model (GPLVM) (Lawrence, 2005) is the non-parametric analogue of our model, and employs Gaussian process priors over the non-linear functions between each layer.”
Gaussian Processes for Big Data (2013, methodology): “Several GP based models involve inference of X , such as the GP latent variable model [Lawrence, 2005, Titsias and Lawrence, 2010] and its extensions [e.g. Damianou et al., 2011, 2012].”
High-Dimensional Probability Estimation with Deep Density Models (2013, methodology): “…characterize the density of data via a low-dimensional embedding, e.g., locally-linear embeddding [Roweis and Saul, 2000], IsoMap [Tenenbaum et al., 2000], the Gaussian process latent variable model [Lawrence, 2005], kernel PCA [Sch¨olkopf et al., 1998], and t-SNE [Van der Maaten and Hinton, 2008].”
Learning deep dynamical models from image pixels (2014, methodology): “structions. In the machine learning literature, there exists a vast number of other well studied nonlinear dimensionality reduction methods such as the Gaussian process latent variable model (GP-LVM) [7], kernel PCA [14], Laplacian Eigenmaps [1] and Locally Linear Embedding [12]. However, all of the”
Distributed optimization of deeply nested systems (2012, background): “Larger speedups would be achievable with other parallel computation models such as MPI in C, and using a distributed architecture (so that cache and other overheads are reduced).”
Bayesian group factor analysis with structured sparsity (2016, methodology): “Although our focus will be on linear maps, we will keep the non-linear possibility open for model extensions, and we will include the GPLVM model in our model comparisons on simulated data.”
Machine learning of linear differential equations using Gaussian processes (2017, background): “Such models generalize latent variable models [24,25,50] using differential equations.”
Using dimensionality reduction to exploit constraints in reinforcement learning (2010, methodology): “We initialise Z with points found by applying PCA as suggested in [14].”
Dynamic Manifold Warping for view invariant action recognition (2011, background): “Note that our goal is different from most latent variable models, which aim to identify τ [19] and sometimes f(·) [5, 21, 22].”
Distributed Gaussian Processes (2015, background): “…in various research areas, including geostatistics (Cressie, 1993), optimisation (Jones et al., 1998; Brochu et al., 2009), data visualisation (Lawrence, 2005), robotics and reinforcement learning (Deisenroth et al., 2015), spatio-temporal mod-MPD acknowledges the support of an Imperial…”
Variational Gaussian Process Dynamical Systems (2011, background): “One promising approach to these time series has been to extend the Gaussian process latent variable model [1, 2] with a dynamical prior for the latent space and seek a maximum a posteriori (MAP) solution for the latent points [3, 4, 5].”
Nonparametric guidance of autoencoder representations using label information (2012, background): “The Gaussian process latent variable model (Lawrence, 2005) addresses this challenge under a Bayesian probabilistic formulation.”