Heteroscedastic Gaussian process regression

By Quoc V. Le, Alex Smola, Stéphane Canu. 2005

246 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Control and Systems Engineering

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Citations in the corpus

Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, background): “Heteroscedasticity has been widely addressed in the GP literature, see e.g., [95], [86], [103].”
What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision? (2017, background): “Heteroscedastic regression, on the other hand, assumes that observation noise can vary with input x [17, 18].”
Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification (2018, unknown): “The heteroscedastic noise [54, 55, 56] can be implemented as extending the output of the neural net as: [f(x,w), σ(2)(x,w)] or [f(x,w),σ(2)(x,w)].”
High-Quality Self-Supervised Deep Image Denoising (2019, methodology): “To fit N (μy,Σy) to the observed noisy training data, we minimize the corresponding negative loglikelihood loss during training [22, 16, 13]:”
Kernel methods and the exponential family (2006, methodology): “In this case the application of the represented theorem gives a heteroscedastic gaussian process (with non-constant variance) as the model of the data, associated with a convex optimization problem (see Le et al. [2005] for details).”
Most likely heteroscedastic Gaussian process regression (2007, background): “Le et al. (2005) also estimate the variance non-parametrically along with the mean of the distribution.”
Uncertainty in Deep Learning (2016, background): “Heteroscedastic regression, on the other hand, assumes that observation noise can vary with input x [Le et al., 2005].”
Decomposition of Uncertainty in Bayesian Deep Learning for Efficient and Risk-sensitive Learning (2017, methodology): “…task, the epistemic and the total uncertainty have a similar behaviour as shown in Figures 2d and 2f. Finally, we note that heteroscedastic GPs (Le et al., 2005) will likely perform similar to BNN+LV in the heteroscedastic task from Figure 2, but they will fail in the other two settings…”
Gaussian process product models for nonparametric nonstationarity (2008, background): “…noise in the Gaussian process, addressed by Goldberg et al. (1998), who model a log-noise term in the covariance function with another Gaussian process, and by Le et al. (2005) who model nonstationary noise by performing regression in the natural parameter space of the exponential family.”
Data Uncertainty Learning in Face Recognition (2020, methodology): “Difficulty of Introducing Data Uncertainty Regression to FR DULrgs is inspired from data uncertainty regression [26, 22] for continuous mapping space X → Y as described in Section 3.”
A probabilistic data-driven model for planar pushing (2017, methodology): “In this paper we explicitly consider the dependence of the noise in the transition dynamics with the input action by using heteroscedastic Gaussian processes introduced by Le and Smola [18].”
Unifying Divergence Minimization and Statistical Inference Via Convex Duality (2006, unknown): “– For ψ(t) = (y, y(2))ψx(x), we obtain the heteroscedastic GP regression estimates of [13].”
Uncertainty-Aware Learning for Zero-Shot Semantic Segmentation (2020, methodology): “The variance is related to the input sample’s uncertainty [37, 43], thus allowing the model to explicitly account for the observation noise of the training data.”
Gaussian Process Training with Input Noise (2011, background): “[5] who proposed a scheme to find the variance via a maximum-a-posteriori estimate set in the exponential family.”