相关论文: Gaussian Processes indexed on the symmetric group:…

Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…

We formulate meta learning using information theoretic concepts; namely, mutual information and the information bottleneck. The idea is to learn a stochastic representation or encoding of the task description, given by a training set, that…

In this paper, we investigate Gaussian process regression models where inputs are subject to measurement error. In spatial statistics, input measurement errors occur when the geographical locations of observed data are not known exactly.…

In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing…

We algorithmically construct multi-output Gaussian process priors which satisfy linear differential equations. Our approach attempts to parametrize all solutions of the equations using Gr\"obner bases. If successful, a push forward Gaussian…

To obtain more accurate model parameters and improve prediction accuracy, we proposed a regularized Kriging model that penalizes the hyperparameter theta in the Gaussian stochastic process, termed the Theta-regularized Kriging. We derived…

Kernel-based machine learning approaches are gaining increasing interest for exploring and modeling large dataset in recent years. Gaussian process (GP) is one example of such kernel-based approaches, which can provide very good performance…

The canonical technique for nonlinear modeling of spatial/point-referenced data is known as kriging in geostatistics, and as Gaussian Process (GP) regression for surrogate modeling and statistical learning. This article reviews many…

Gaussian processes are Bayesian non-parametric models used in many areas. In this work, we propose a Non-stationary Heteroscedastic Gaussian process model which can be learned with gradient-based techniques. We demonstrate the…

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,…

Let $(G(X_j))_{j\geq1}$ be a multivariate subordinated Gaussian process, which exhibits long-range dependence. We study the asymptotic behaviour of the corresponding sequential empirical process under two different types of subordination.…

Approximation of functions satisfying partial differential equations (PDEs) is paramount for simulation of physical fluid flows and other problems in physics. Recently, physics-informed machine learning approaches have proven useful as a…

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 well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

Analyzing massive spatial datasets using Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental heath. We present a…

Gaussian process priors are a popular choice for Bayesian analysis of regression problems. However, the implementation of these models can be complex, and ensuring that the implementation is correct can be challenging. In this paper we…

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.…

This article proposes a new kriging that has a rational form. It is shown that the generalized least squares estimate of the mean from rational kriging is much more well behaved than that from ordinary kriging. Parameter estimation and…

Gaussian process modeling is a standard tool for building emulators for computer experiments, which are usually used to study deterministic functions, for example, a solution to a given system of partial differential equations. This work…