Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)

By Carl E. Rasmussen, Christopher K. I. Williams. 2005

4,392 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

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In Probabilistic & Bayesian Methods

Citations in the corpus

Identifying and attacking the saddle point problem in high-dimensional non-convex optimization (2014, background): “(Rasmussen and Williams, 2005) have shown that such a random error function would have many local minima and maxima, with high probability over the choice of the function, but saddles would occur with negligible probability.”
Training generative neural networks via Maximum Mean Discrepancy optimization (2015, methodology): “Following Gretton et al. [2], we used a radial basis function (RBF) kernel, but also evaluated the rational quadratic (RQ) kernel [9] and Laplacian kernel, but found that the RBF performed best in the parameter ranges we evaluated.”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Readers who are interested particularly in the typical applications of kernels in machine learning, e.g., support vector machines (SVMs) and Gaussian processes (GPs), are encouraged to read Cucker and Smale (2002), Burges (1998), Rasmussen and Williams (2005) and references therein.”
A Survey on Neural Architecture Search (2019, methodology): “In their approach they model the surrogate with a Gaussian process (Rasmussen and Williams, 2006) and use expected improvement as the acquisition function (Mockus et al.”
An evaluation of adaptive surrogate modeling based optimization with two benchmark problems (2014, methodology): “Training an accurate surrogate model needs adequate inputeoutput data, which are obtained by running the simulation model with different sets of parameters selected in the feasible parameter space.”
Raiders of the Lost Architecture: Kernels for Bayesian Optimization in Conditional Parameter Spaces (2014, background): “The most common choice of prior distributi on are Gaussian processes ( GPs [2]), as they are powerful and flexible models for which the margina l a d conditional distributions can be computed efficiently.”
Reinforcement learning in robotics: A survey (2013, background): “A prominent example that has found much use within reinforcement learning is Gaussian process regression (Rasmussen and Williams, 2006).”
Kernel Mean Shrinkage Estimators (2014, background): “…of high frequency components of ˆ µ ( i.e. , contribution of ˆ µ along the directions corresponding to smaller γ i ) when ˆ µ is expanded in terms of the eigenfunctions of the empirical covariance operator, which are nothing but the kernel PCA basis (see Rasmussen and Williams (2006, Section 4.3)).”
Variational Auto-Regressive Gaussian Processes for Continual Learning (2020, background): “Gaussian Processes (GPs) provide a flexible non-parametric framework to perform probabilistic inference [24].”
Continual Deep Learning by Functional Regularisation of Memorable Past (2020, methodology): “1 or Chapter 2 in Rasmussen and Williams [24]): mlin(x) := fwlin(x), κlin(x,x ′) := φ(x)Σlin φ(x ′), (2) where wlin is simply the Maximum A Posteriori (MAP) estimate of the linear model, and Σ−1 lin := N ∑”
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.”
Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference (2015, methodology): “Assume we are given a covariance function of the form K ( x , y ) = p ( w ) p ( b ) σ ( w T x + b ) σ ( w T y + b ) d w d b with some element-wise non-linearity σ ( · ) and distributions p ( w ) , p ( b ) .”
Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling (2018, neutral): “Gaussian processes [22] are a gold-standard method for modeling distributions over non-linear continuous functions, and a natural baseline.”