Related papers: Fast covariance parameter estimation of spatial Ga…
Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…
Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…
In spatial statistics, fast and accurate parameter estimation, coupled with a reliable means of uncertainty quantification, can be challenging when fitting a spatial process to real-world data because the likelihood function might be slow…
Multi-model ensemble analysis integrates information from multiple climate models into a unified projection. However, existing integration approaches based on model averaging can dilute fine-scale spatial information and incur bias from…
Gaussian Processes (GP) have become popular machine-learning methods for kernel-based learning on datasets with complicated covariance structures. In this paper, we present a novel extension to the GP framework using a contaminated normal…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…
The proliferation of capable and efficient machine learning (ML) models marks one of the strongest methodological shifts in signal processing (SP) in its nearly 100-year history. ML models support the development of SP systems that…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
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…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
Spatial generalized linear mixed models (SGLMMs) are popular and flexible models for non-Gaussian spatial data. They are useful for spatial interpolations as well as for fitting regression models that account for spatial dependence, and are…
Gaussian processes (GPs), or distributions over arbitrary functions in a continuous domain, can be generalized to the multi-output case: a linear model of coregionalization (LMC) is one approach. LMCs estimate and exploit correlations…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…
Neural-net-induced Gaussian process (NNGP) regression inherits both the high expressivity of deep neural networks (deep NNs) as well as the uncertainty quantification property of Gaussian processes (GPs). We generalize the current NNGP to…
Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…
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…
The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…