Related papers: Efficient Two-Stage Gaussian Process Regression Vi…

When the data are sparse, optimization of hyperparameters of the kernel in Gaussian process regression by the commonly used maximum likelihood estimation (MLE) criterion often leads to overfitting. We show that choosing hyperparameters (in…

Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework -- GPatt -- enabling automatic pattern extrapolation with Gaussian processes on large…

Gaussian process (GP) regression provides a strategy for accelerating saddle point searches on high-dimensional energy surfaces by reducing the number of times the energy and its derivatives with respect to atomic coordinates need to be…

Frequency response function (FRF) estimation is a classical subject in system identification. In the past two decades, there have been remarkable advances in developing local methods for this subject, e.g., the local polynomial method,…

Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides…

Radial Basis Function (RBF), or Gaussian, kernels are among the most widely used parametric kernels in machine learning, particularly in methods such as Support Vector Machines (SVM) and kernel-based subspace approaches. The kernel…

Current remote sensing image classification problems have to deal with an unprecedented amount of heterogeneous and complex data sources. Upcoming missions will soon provide large data streams that will make land cover/use classification…

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…

Gaussian process (GP) regression is a fundamental tool in Bayesian statistics. It is also known as kriging and is the Bayesian counterpart to the frequentist kernel ridge regression. Most of the theoretical work on GP regression has focused…

This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean…

In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

This work presents a novel method for extracting potential barrier distributions from experimental fusion cross sections. We utilize a simple Gaussian process regression (GPR) framework to model the observed cross sections as a function of…

In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger…

Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…

We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…

We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…

Gaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to re-formulate the matrix-variate Gaussian distribution as a multivariate normal distribution.…

We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…

Vibrational properties of molecular crystals are constantly used as structural fingerprints, in order to identify both the chemical nature and the structural arrangement of molecules. The simulation of these properties is typically very…

We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression which provides a…