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Approximate Bayesian computation (ABC) can be used for model fitting when the likelihood function is intractable but simulating from the model is feasible. However, even a single evaluation of a complex model may take several hours,…
Gaussian processes (GP) are powerful tools for probabilistic modeling purposes. They can be used to define prior distributions over latent functions in hierarchical Bayesian models. The prior over functions is defined implicitly by the mean…
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…
Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often a few parameters are sufficient to parameterize the covariance…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…
Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of…
In many areas of the observational and experimental sciences data is scarce. Data observation in high-energy astrophysics is disrupted by celestial occlusions and limited telescope time while data derived from laboratory experiments in…
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…
Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…
We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can…
Gaussian process (GP) covariance function is proposed as a matching tool in GPMatch within a full Bayesian framework under relatively weaker causal assumptions. The matching is accomplished by utilizing GP prior covariance function to…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…
Gaussian processes (GPs) play an essential role in biostatistics, scientific machine learning, and Bayesian optimization for their ability to provide probabilistic predictions and model uncertainty. However, GP inference struggles to scale…
The Gaussian process (GP) model, which has been extensively applied as priors of functions, has demonstrated excellent performance. The specification of a large number of parameters affects the computational efficiency and the feasibility…
Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…
The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…