Related papers: Gaussian Process Subspace Regression for Model Red…
Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each…
Gaussian Processes (GPs) have been widely used in machine learning to model distributions over functions, with applications including multi-modal regression, time-series prediction, and few-shot learning. GPs are particularly useful in the…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…
It is often of interest to infer lower-dimensional structure underlying complex data. As a flexible class of non-linear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…
This article presents a novel approach to construct Intrinsic Gaussian Processes for regression on unknown manifolds with probabilistic metrics (GPUM) in point clouds. In many real world applications, one often encounters high dimensional…
In spite of the diverse literature on nonstationary spatial modeling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets…
Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
Gaussian processes are used in many machine learning applications that rely on uncertainty quantification. Recently, computational tools for working with these models in geometric settings, such as when inputs lie on a Riemannian manifold,…
Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…
Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…
In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees…
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…
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…
This paper proposes an online learning method of Gaussian process state-space model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that represents unknown state transition and/or measurement models as Gaussian processes…
Gaussian process (GP) regression is a Bayesian nonparametric method for regression and interpolation, offering a principled way of quantifying the uncertainties of predicted function values. For the quantified uncertainties to be…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…