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This paper focuses on the problem of determining as large a region as possible where a function exceeds a given threshold with high probability. We assume that we only have access to a noise-corrupted version of the function and that…
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.…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
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…
Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…
We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…
We propose a novel training objective for GPs constructed using lower-dimensional linear projections of the data, referred to as \emph{projected likelihood} (PL). We provide a closed-form expression for the information loss related to the…
This paper is concerned with the problem of how to speed up computation for Gaussian process models trained on autocorrelated data. The Gaussian process model is a powerful tool commonly used in nonlinear regression applications. Standard…
This paper is an overview of the classical level crossing problem which is studied extensively in the literature and is fundamental in many branches of applied probability. We discuss a number of approximations with an emphasis on their…
In this paper we introduce a novel model for Gaussian process (GP) regression in the fully Bayesian setting. Motivated by the ideas of sparsification, localization and Bayesian additive modeling, our model is built around a recursive…
While the analysis of airborne laser scanning (ALS) data often provides reliable estimates for certain forest stand attributes -- such as total volume or basal area -- there is still room for improvement, especially in estimating…
As the amount and complexity of available data increases, the need for robust statistical learning becomes more pressing. To enhance resilience against model misspecification, the generalized posterior inference method adjusts the…
Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…
Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…