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Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and…

Multi-output Gaussian process (MGP) is commonly used as a transfer learning method to leverage information among multiple outputs. A key advantage of MGP is providing uncertainty quantification for prediction, which is highly important for…

Modeling and inferring spatial relationships and predicting missing values of environmental data are some of the main tasks of geospatial statisticians. These routine tasks are accomplished using multivariate geospatial models and the…

Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…

In this paper, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model…

Motivated by the need for computationally tractable spatial methods in neuroimaging studies, we develop a distributed and integrated framework for estimation and inference of Gaussian process model parameters with ultra-high-dimensional…

Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…

This paper presents a novel extension of multi-task Gaussian Cox processes for modeling multiple heterogeneous correlated tasks jointly, e.g., classification and regression, via multi-output Gaussian processes (MOGP). A MOGP prior over the…

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of…

Bayesian spatial modeling provides a flexible framework for whole-brain fMRI analysis by explicitly incorporating spatial dependencies, overcoming the limitations of traditional massive univariate approaches that lead to information waste.…

Gaussian processes (GP) are a versatile tool in machine learning and computational science. We here consider the case of multi-output Gaussian processes (MOGP) and present low-rank approaches for efficiently computing the posterior mean of…

Shape-constrained symbolic regression (SCSR) allows to include prior knowledge into data-based modeling. This inclusion allows to ensure that certain expected behavior is better reflected by the resulting models. The expected behavior is…

This paper considers the surrogate modeling of a complex numerical code in a multifidelity framework when the code output is a time series. Using an experimental design of the low-and high-fidelity code levels, an original Gaussian process…

Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…

This review article focuses on regularised estimation procedures applicable to geostatistical and spatial econometric models. These methods are particularly relevant in the case of big geospatial data for dimensionality reduction or model…

A multivariate quantile regression model with a factor structure is proposed to study data with many responses of interest. The factor structure is allowed to vary with the quantile levels, which makes our framework more flexible than the…

We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…

Gaussian processes (GPs) are a popular class of Bayesian nonparametric models, but its training can be computationally burdensome for massive training datasets. While there has been notable work on scaling up these models for big data,…

Spatial functional data arise in many settings, such as particulate matter curves observed at monitoring stations and age population curves at each areal unit. Most existing functional regression models have limited applicability because…

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…