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Gaussian variational approximations are widely used for summarizing posterior distributions in Bayesian models, especially in high-dimensional settings. However, a drawback of such approximations is the inability to capture skewness or more…

Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…

Statistical modeling for massive spatial data sets has generated a substantial literature on scalable spatial processes based upon Vecchia's approximation. Vecchia's approximation for Gaussian process models enables fast evaluation of the…

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

Gaussian processes are flexible probabilistic regression models which are widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, full-scale approximations…

The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…

We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…

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 general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…

Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…

Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…

We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to…

Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

Gaussian processes are flexible, probabilistic, non-parametric models widely used in machine learning and statistics. However, their scalability to large data sets is limited by computational constraints. To overcome these challenges, we…

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…

Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true…