Bayesian Gaussian Process Latent Variable Model

By Michalis K. Titsias, Neil D. Lawrence. 2010

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Citations in the corpus

Variational Inference: A Review for Statisticians (2016, background): “…2004; Barber and Chiappa 2006; Archambeau et al. 2007a, 2007b; Johnson and Willsky 2014; Foti et al. 2014), robust models (Tipping and Lawrence 2005; Wang and Blei 2015), and Gaussian process models (Titsias and Lawrence 2010; Damianou, Titsias, and Lawrence 2011; Hensman, Fusi, and Lawrence 2013).”
Manifold Gaussian Processes for regression (2014, background): “This kind of GP training is also analytically intractable, although approximations exist (Lawrence, 2005; Wang et al., 2008; McHutchon and Rasmussen, 2011; Titsias and Lawrence, 2010).”
High-Dimensional Probability Estimation with Deep Density Models (2013, methodology): “Other approaches, such as the Bayesian GP-LVM [Titsias and Lawrence, 2010], characterize the manifold implicitly in terms of a nonlinear mapping from a representation space to the observed space.”
Meta Reinforcement Learning with Latent Variable Gaussian Processes (2018, methodology): “A Bayesian extension (BG-PLVM) was introduced in [31] where inference over the latent variable is performed using variational inference.”
Machine learning of linear differential equations using Gaussian processes (2017, background): “Such models generalize latent variable models [24,25,50] using differential equations.”
A physics-aware, probabilistic machine learning framework for coarse-graining high-dimensional systems in the Small Data regime (2019, methodology): “Apart from nonlinear models, an interesting possibility involves Bayesian nonparametric extensions, whereby each uf,i can be expressed using an independent Gaussian Process in a fashion analogous to GP-LVMs (Lawrence, 2005; Titsias and Lawrence, 2010).”
Automatic model construction with Gaussian processes (2014, methodology): “The latent positions X in the GP-LVM are typically obtained by maximum a posteriori estimation or variational Bayesian inference (Titsias and Lawrence, 2010), placing a single fixed spherical Gaussian prior on x.”
Structured Bayesian Gaussian process latent variable model: applications to data-driven dimensionality reduction and high-dimensional inversion (2018, methodology): “This approach may be seen as combining the “collapsed” bound of [20] to compute L and the “uncollapsed” bound for L∗.”
Parametric Gaussian process regression for big data (2017, background): “In addition, Gaussian process latent variable [30] model (GPLVM) can be seen as an unsupervised version of the regression problem studied so far.”
Variational Auto-encoded Deep Gaussian Processes (2015, methodology): “A variational approximation technique developed for Bayesian Gaussian Process Latent variable Model (BGPLVM) (Titsias & Lawrence, 2010) can be applied to obtain a lower bound of these free energy terms.”
Variational Gaussian Process Dynamical Systems (2011, methodology): “In this paper we build on recent developments in variational approximations for Gaussian processes [7, 8] to introduce a variational Gaussian process dynamical system (VGPDS) where latent variables are approximately marginalized through optimization of a rigorous lower bound on the marginal…”
A Unifying Framework for Gaussian Process Pseudo-Point Approximations using Power Expectation Propagation (2016, methodology): “, 2015), latent variable models (Titsias and Lawrence, 2010) and state space models (Frigola et al.”
Manifold GPLVMs for discovering non-Euclidean latent structure in neural data (2020, methodology): “For non-Euclidean manifolds, inference in mGPLVMs poses two major problems.”