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Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…
In the present paper we continue the investigation of solutions to higher-order heat-type equations with random initial conditions, which play the important role in many applied areas. We consider the random initial conditions given by…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
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…
Gaussian processes~(Kriging) are interpolating data-driven models that are frequently applied in various disciplines. Often, Gaussian processes are trained on datasets and are subsequently embedded as surrogate models in optimization…
In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…
In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then…
We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
Aggregated data is commonplace in areas such as epidemiology and demography. For example, census data for a population is usually given as averages defined over time periods or spatial resolutions (cities, regions or countries). In this…
Gaussian Process Regression (GPR) is widely used in statistics and machine learning for prediction tasks requiring uncertainty measures. Its efficacy depends on the appropriate specification of the mean function, covariance kernel function,…
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…
Multi-fidelity Gaussian process is a common approach to address the extensive computationally demanding algorithms such as optimization, calibration and uncertainty quantification. Adaptive sampling for multi-fidelity Gaussian process is a…
The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…
This paper describes an expectation propagation (EP) method for multi-class classification with Gaussian processes that scales well to very large datasets. In such a method the estimate of the log-marginal-likelihood involves a sum across…
We introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo…
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…
In applications of Gaussian processes where quantification of uncertainty is of primary interest, it is necessary to accurately characterize the posterior distribution over covariance parameters. This paper proposes an adaptation of the…
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…
Despite the availability of ever more data enabled through modern sensor and computer technology, it still remains an open problem to learn dynamical systems in a sample-efficient way. We propose active learning strategies that leverage…