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Multiscale modeling is a systematic approach to describe the behavior of complex systems by coupling models from different scales. The approach has been demonstrated to be very effective in areas of science as diverse as materials science,…
The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…
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…
Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing…
Gaussian processes (GPs) are widely used as surrogate models for complicated functions in scientific and engineering applications. In many cases, prior knowledge about the function to be approximated, such as monotonicity, is available and…
Gaussian process is one of the most popular non-parametric Bayesian methodologies for modeling the regression problem. It is completely determined by its mean and covariance functions. And its linear property makes it relatively…
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…
Markov random fields (MRFs) have been widely used as prior models in various inverse problems such as tomographic reconstruction. While MRFs provide a simple and often effective way to model the spatial dependencies in images, they suffer…
In this paper an approach for decreasing the computational effort required for the split-step Fourier method (SSFM) is introduced. It is shown that using the sparsity property of the simulated signals, the compressive sampling algorithm can…
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…
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…
Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…
Gaussian conditional random fields (GCRF) are a well-known used structured model for continuous outputs that uses multiple unstructured predictors to form its features and at the same time exploits dependence structure among outputs, which…
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…
Gaussian processes (GPs) are typically criticised for their unfavourable scaling in both computational and memory requirements. For large datasets, sparse GPs reduce these demands by conditioning on a small set of inducing variables…
We propose a determinant-free approach for simulation-based Bayesian inference in high-dimensional Gaussian models. We introduce auxiliary variables with covariance equal to the inverse covariance of the model. The joint probability of the…
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 surrogates are a popular alternative to directly using computationally expensive simulation models. When the simulation output consists of many responses, dimension-reduction techniques are often employed to construct these…
This paper addresses the challenge of reconstructing full-field structural mode shapes from sparse sensor data. While Gaussian Process Regression (GPR) offers a robust non-parametric framework for spatial interpolation and uncertainty…