Related papers: Scaling Gaussian Processes with Derivative Informa…
We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the…
Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…
We develop a scalable deep non-parametric generative model by augmenting deep Gaussian processes with a recognition model. Inference is performed in a novel scalable variational framework where the variational posterior distributions are…
Although it is widely known that Gaussian processes can be conditioned on observations of the gradient, this functionality is of limited use due to the prohibitive computational cost of $\mathcal{O}(N^3 D^3)$ in data points $N$ and…
In this paper, we study the problem of deriving fast and accurate classification algorithms with uncertainty quantification. Gaussian process classification provides a principled approach, but the corresponding computational burden is…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…
Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…
We investigate the use of derivative information for Batch Active Learning in Gaussian Process regression models. The proposed approach employs the predictive covariance matrix for selection of data batches to exploit full correlation of…
Gaussian process classification is a popular method with a number of appealing properties. We show how to scale the model within a variational inducing point framework, outperforming the state of the art on benchmark datasets. Importantly,…
Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…
Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…
Variational methods have been recently considered for scaling the training process of Gaussian process classifiers to large datasets. As an alternative, we describe here how to train these classifiers efficiently using expectation…
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…
We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…