Related papers: Recyclable Gaussian Processes
We present a method to approximate Gaussian process regression models for large datasets by considering only a subset of the data. Our approach is novel in that the size of the subset is selected on the fly during exact inference with…
We present a non-parametric prognostic framework for individualized event prediction based on joint modeling of both longitudinal and time-to-event data. Our approach exploits a multivariate Gaussian convolution process (MGCP) to model the…
This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…
In this paper, we discuss vector-valued Gaussian processes for the approximation of divergence- or rotation-free functions. We establish the theory for such Gaussian processes, then link the theory to multivariate approximation theory, and…
Spectral approximation and variational inducing learning for the Gaussian process are two popular methods to reduce computational complexity. However, in previous research, those methods always tend to adopt the orthonormal basis functions,…
It is now known that an extended Gaussian process model equipped with rescaling can adapt to different smoothness levels of a function valued parameter in many nonparametric Bayesian analyses, offering a posterior convergence rate that is…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
To scale Gaussian processes (GPs) to large data sets we introduce the robust Bayesian Committee Machine (rBCM), a practical and scalable product-of-experts model for large-scale distributed GP regression. Unlike state-of-the-art sparse GP…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
In applications of Gaussian processes where quantification of uncertainty is a strict requirement, it is necessary to accurately characterize the posterior distribution over Gaussian process covariance parameters. Normally, this is done by…
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…
The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…
Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…
Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as…
We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and…
Gaussian Processes (GPs) are powerful non-parametric Bayesian regression models that allow exact posterior inference, but exhibit high computational and memory costs. In order to improve scalability of GPs, approximate posterior inference…