Related papers: Consistent Online Gaussian Process Regression With…
Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…
Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…
Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…
Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. In this paper, we provide a general framework for understanding the frequentist coverage of point-wise and…
Intelligent real-world systems critically depend on expressive information about their system state and changing operation conditions, e.g., due to variation in temperature, location, wear, or aging. To provide this information, online…
Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…
We present an approximate Bayesian inference approach for estimating the intensity of an inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function. Augmenting the…
We propose a nested Gaussian process (nGP) as a locally adaptive prior for Bayesian nonparametric regression. Specified through a set of stochastic differential equations (SDEs), the nGP imposes a Gaussian process prior for the function's…
Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…
This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region.…
Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…
Devising optimal operating strategies for a compressor station relies on the knowledge of compressor characteristics. As the compressor characteristics change with time and use, it is necessary to provide accurate models of the…
Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models…
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…
Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…
In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate…
There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…
We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However,…
We study posterior contraction rates for a class of deep Gaussian process priors applied to the nonparametric regression problem under a general composition assumption on the regression function. It is shown that the contraction rates can…
We are interested in probabilistic prediction in online settings in which data does not follow a probability distribution. Our work seeks to achieve two goals: (1) producing valid probabilities that accurately reflect model confidence; and…