Related papers: Stochastic Gradient MCMC for Massive Geostatistica…

In this paper, we investigate Gaussian process regression models where inputs are subject to measurement error. In spatial statistics, input measurement errors occur when the geographical locations of observed data are not known exactly.…

This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…

We introduce a class of scalable Bayesian hierarchical models for the analysis of massive geostatistical datasets. The underlying idea combines ideas on high-dimensional geostatistics by partitioning the spatial domain and modeling the…

There has been recent interest in developing scalable Bayesian sampling methods such as stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) for big-data analysis. A standard SG-MCMC algorithm simulates samples…

Missing values are common in many real-life datasets. However, most of the current machine learning methods can not handle missing values. This means that they should be imputed beforehand. Gaussian Processes (GPs) are non-parametric models…

Large spatial datasets with non-Gaussian responses are increasingly common in environmental monitoring, ecology, and remote sensing, yet scalable Bayesian inference for such data remains challenging. Markov chain Monte Carlo (MCMC) methods…

The log Gaussian Cox process is a flexible class of point pattern models for capturing spatial and spatio-temporal dependence for point patterns. Model fitting requires approximation of stochastic integrals which is implemented through…

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Gaussian Processes (GPs) provide a powerful framework for making predictions and understanding uncertainty for classification with kernels and Bayesian non-parametric learning. Building such models typically requires strong prior knowledge…

We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely…

Inferring the infinitesimal rates of continuous-time Markov chains (CTMCs) is a central challenge in many scientific domains. This task is hindered by three factors: quadratic growth in the number of rates as the CTMC state space expands,…

In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ…

Markov chain Monte Carlo (MCMC) simulation methods are widely used to assess parametric uncertainties of hydrologic models conditioned on measurements of observable state variables. However, when the model is CPU-intensive and…

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…

We investigate two options for performing Bayesian inference on spatial log-Gaussian Cox processes assuming a spatially continuous latent field: Markov chain Monte Carlo (MCMC) and the integrated nested Laplace approximation (INLA). We…

Stochastic gradient MCMC (SGMCMC) offers a scalable alternative to traditional MCMC, by constructing an unbiased estimate of the gradient of the log-posterior with a small, uniformly-weighted subsample of the data. While efficient to…

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…

Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited…

We present a two-stage Metropolis-Hastings algorithm for sampling probabilistic models, whose log-likelihood is computationally expensive to evaluate, by using a surrogate Gaussian Process (GP) model. The key feature of the approach, and…