Warped Gaussian Processes

By Edward Snelson, Carl E. Rasmussen, Zoubin Ghahramani. 2003

390 citations recorded by the source corpus.

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Citations in the corpus

Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, background): “There are many other examples of nonstationary covariance functions [3], [22], [54], [70], [118], [121], [126], [132] that have been proposed for GP regression along with closely related output warping techniques [141] that can also model certain kinds of nonstationary processes.”
Deep Gaussian Processes (2012, background): “…expressive variants, for example by considering sophisticated covariance functions [Durrande et al., 2011, G¨onen and Alpaydin, 2011] or by embedding GPs in more complex probabilistic structures [Snelson et al., 2004, Wilson et al., 2012] able to learn more powerful representations of the data.”
Manifold Gaussian Processes for regression (2014, methodology): “One way to implement this second approach is to transform the output space as in the Warped GP (Snelson et al., 2004).”
Neural Spline Flows (2019, background): “For instance, monotonic warping functions with a tractable Jacobian determinant are useful for supervised learning [50].”
Deep Gaussian Processes for Regression using Approximate Expectation Propagation (2016, background): “A special case of DGPs when L = 2 and the sole hidden layer h1 is only one dimensional is warped GPs (Snelson et al., 2004; Lázaro-Gredilla, 2012).”
Gaussian Processes for Regression and Optimisation (2007, methodology): “We have seen methods to deal with input-dependent noise [20] and non-Gaussian noise [72].”
Most likely heteroscedastic Gaussian process regression (2007, methodology): “W: The synthetic data originally used by Williams (1996): 200 input xi are drawn from a uniform distribution on [0, π].”
Learning Scalable Deep Kernels with Recurrent Structure (2016, background): “We remark that combinations of GPs with nonlinear functions have also been considered in the past in a slightly diﬀerent setting of warped regression targets (Snelson et al., 2003; Wilson and Ghahramani, 2010; Lázaro-Gredilla, 2012).”
Multi-task warped Gaussian process for personalized age estimation (2010, background): “In this section, we briefly review the Gaussian process (GP) [25] and the warped Gaussian process (WGP) [26].”
Variational Implicit Processes (2018, background): “In the world of nonparametric models, Gaussian Processes (GPs) [75] provides a principled and ﬂexible probabilistic framework for Bayesian inference over functions.”
Scalable Inference for Gaussian Process Models with Black-Box Likelihoods (2015, methodology): “Here we note that [6] showed that automated variational inference performed competitively when compared to hand-crafted methods for warped GPs [15].”
Copulas in Machine Learning (2013, unknown): “[49].”
Copula Processes (2010, methodology): “To do this, we ﬁt a Gaussian copula process by using a type of Warped Gaussian Process [15].”
Variational Auto-encoded Deep Gaussian Processes (2015, background): “One line of recent research to address this limitation focused on function composition (Snelson et al., 2004; Calandra et al., 2014).”