Hierarchical Gaussian process latent variable models

By Neil D. Lawrence, Andrew J. Moore. 2007

227 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Control and Systems Engineering, Signal Processing

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Citations in the corpus

Deep Gaussian Processes (2012, methodology): “For our ﬁrst demonstration on real data we recreate a motion capture data experiment from Lawrence and Moore [2007].”
Deep Neural Networks as Gaussian Processes (2017, background): “The correspondence between infinite neural networks and GPs was first noted by Neal (1994a;b). Williams (1997) computed analytic GP kernels for single hidden-layer neural networks with error function or Gaussian nonlinearities and noted the use of the GP prior for exact Bayesian inference in regress”
On Exact Computation with an Infinitely Wide Neural Net (2019, background): “Another line of work built probabilistic graphical models (PGMs) which uses kernel as a component [Damianou and Lawrence, 2013, Lawrence and Moore, 2007, Van der Wilk et al., 2017, Kumar et al., 2018, Blomqvist et al., 2018].”
Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation (2019, methodology): “Many previous works have exploited this DNN-GP correspondence implicitly or explicitly to build new models (Cho & Saul, 2009; Lawrence & Moore, 2007; Damianou & Lawrence, 2013; Wilson et al., 2016b;a; Bradshaw et al., 2017; van der Wilk et al., 2017; Kumar et al., 2018; Blomqvist et al., 2018;…”
Bayesian Deep Convolutional Networks with Many Channels are Gaussian Processes (2018, background): “[21] Neil D Lawrence and Andrew J Moore.”
Avoiding pathologies in very deep networks (2014, methodology): “The first instance of deep GPs being used in practice was [Lawrence and Moore, 2007], who presented a model called “hierarchical GP-LVMs”, in which time was mapped through a composition of multiple GPs to produce observations. The term “deep Gaussian processes” was first used by Damianou and Lawrenc”
Automatic model construction with Gaussian processes (2014, background): “The first instance of deep GPs being used in practice was (Lawrence and Moore, 2007), who presented a model called “hierarchical GP-LVMs”, in which time was mapped through a composition of multiple GPs to produce observations.”
Two Distributed-State Models For Generating High-Dimensional Time Series (2011, background): “, 2007) and hierarchical GP-LVMs (Lawrence and Moore, 2007) address this limitation.”
3D Human Pose Estimation from a Single Image via Distance Matrix Regression (2016, methodology): “More sophisticated models allowing to represent larger deformations include spectral embedding [43], Gaussian Mixtures on Euclidean or Riemannian manifolds [15, 41] and Gaussian processes [22, 48, 54].”
Manifold Relevance Determination (2012, background): “For the dynamical scenario we follow Damianou et al. (2011); Lawrence & Moore (2007) and choose the prior on the latent space to depend on the observation times t ∈ R N , e.g. a GP with a covariance function k = k ( t, t (cid:48) ) .”
A Fine-Grained Spectral Perspective on Neural Networks (2019, background): “This connection was exploited implicitly or explicitly to build new models [15, 32, 16, 61, 62, 12, 58, 31, 10, 11, 20, 39, 34].”
Dynamical binary latent variable models for 3D human pose tracking (2010, methodology): “For the implementation of the GPLVM in [13] an annealed particle filter with 5 layers of annealing and 500 particles per layer was used. vated by comparison to the original results reported in [12].”
Bayesian Optimization and Semiparametric Models with Applications to Assistive Technology (2014, background): “The authors address this by setting points in the latent space where transitions are possible to be neighbors in the LLE prior. van der Maaten [2009] similarly uses a dimensionality reduction technique (t-SNE [van der Maaten and Hinton, 2008]) to initialize the GPLVM and as the prior for the latent ”
Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processes (2019, background): “[33] Neil D Lawrence and Andrew J Moore.”
Latent spaces for dynamic movement primitives (2009, background): “For example, Lawrence and Moore [15] define hierarchical priors on Z with suitable adaptation of the likelihood to explicitly model hierarchical dependencies in the data dimensions.”
Variational Gaussian Process Dynamical Systems (2011, background): “[5, 3]) marginalise out only F and seek a MAP solution for X .”
Generalizing motion edits with Gaussian processes (2009, methodology): “Lawrence and Moore visualize human animation with hierarchies of Gaussian process latent variable models [Lawrence and Moore 2007].”
Learning GP-BayesFilters via Gaussian process latent variable models (2009, methodology): “Other alternatives for non-linear embedding in the context of dynamical systems are hierarchical GPLVMs (Lawrence and Moore 2007) and action respecting embeddings (ARE) (Bowling et al.”