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Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…

Machine Learning · Computer Science 2025-03-04 Sarem Seitz

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…

Machine Learning · Statistics 2015-03-23 Yarin Gal , Richard Turner

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…

Computation · Statistics 2021-03-08 Karla Monterrubio-Gómez , Sara Wade

Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…

Methodology · Statistics 2018-01-17 Jean Daunizeau

We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…

Machine Learning · Statistics 2018-11-06 Edwin V. Bonilla , Karl Krauth , Amir Dezfouli

Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…

Computation · Statistics 2019-11-26 Linda S. L. Tan , Nial Friel

Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…

Machine Learning · Computer Science 2022-12-21 Felix Leibfried , Vincent Dutordoir , ST John , Nicolas Durrande

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

Machine Learning · Statistics 2025-11-26 Jonas Latz , Aretha L. Teckentrup , Simon Urbainczyk

We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…

Artificial Intelligence · Computer Science 2013-01-30 Kevin Murphy

We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…

Data Analysis, Statistics and Probability · Physics 2018-08-15 Philipp Batz , Andreas Ruttor , Manfred Opper

As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…

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…

Machine Learning · Computer Science 2018-09-11 Linfeng Liu , Liping Liu

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

Machine Learning · Statistics 2018-02-02 Xiuming Liu , Dave Zachariah , Edith C. H. Ngai

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…

Machine Learning · Computer Science 2021-04-07 Bingxin Zhou , Junbin Gao , Minh-Ngoc Tran , Richard Gerlach

An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…

Artificial Intelligence · Computer Science 2013-04-10 Ross D. Shachter

While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…

Machine Learning · Statistics 2015-09-08 David A. Knowles

Link prediction aims to reveal missing edges in a graph. We address this task with a Gaussian process that is transformed using simplified graph convolutions to better leverage the inductive bias of the domain. To scale the Gaussian process…

Machine Learning · Computer Science 2020-02-12 Felix L. Opolka , Pietro Liò

Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as…

Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such…

Machine Learning · Statistics 2017-11-30 Vincent Adam

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models…