Related papers: Complex-Valued Gaussian Processes for Regression
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 regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
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…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…
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…
Gaussian Process Regression (GPR) is a powerful and elegant method for learning complex functions from noisy data with a wide range of applications, including in safety-critical domains. Such applications have two key features: (i) they…
This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched…
We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
We introduce CUTS-GPR, a new method for performing numerically exact Gaussian process regression (GPR) in high-dimensional settings. The key component of CUTS-GPR is an extremely fast kernel matrix-vector product, which exhibits near-linear…
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…
We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and…
The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for…
The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation…
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…
Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…
Gaussian Process Regression (GPR) is a powerful tool for nonparametric regression, but its application in a fully Bayesian fashion in high-dimensional settings is hindered by two primary challenges: the difficulty of variable selection and…
Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are…