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The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…

Computation · Statistics 2012-09-04 Björn Bornkamp

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 probabilistic and non-parametric…

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…

Numerical Analysis · Mathematics 2026-05-19 Christopher Beattie , David Higdon , Leanna House , Colby Stakun-Pickering , Jared Clark

Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. An extension of this framework to include multiplicative interactions between the…

Machine Learning · Statistics 2019-01-01 Daniel J. Tait , Bruce J. Worton

Gaussian process (GP) surrogate modeling for large computer experiments is limited by cubic runtimes, especially with data from stochastic simulations with input-dependent noise. A popular workaround to reduce computational complexity…

Methodology · Statistics 2022-06-01 D Austin Cole , Robert B Gramacy , Mike Ludkovski

Gaussian processes (GPs) are a popular class of Bayesian nonparametric models, but its training can be computationally burdensome for massive training datasets. While there has been notable work on scaling up these models for big data,…

Methodology · Statistics 2023-11-16 Kevin Li , Simon Mak

Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…

Machine Learning · Computer Science 2025-07-08 Jonathan Wenger , Kaiwen Wu , Philipp Hennig , Jacob R. Gardner , Geoff Pleiss , John P. Cunningham

Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the…

Machine Learning · Statistics 2018-01-10 Marton Havasi , José Miguel Hernández-Lobato , Juan José Murillo-Fuentes

Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While…

Machine Learning · Computer Science 2024-11-01 Tristan Cinquin , Marvin Pförtner , Vincent Fortuin , Philipp Hennig , Robert Bamler

Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…

Machine Learning · Computer Science 2021-02-26 Juan Maroñas , Oliver Hamelijnck , Jeremias Knoblauch , Theodoros Damoulas

Gaussian processes (GPs) play an essential role in biostatistics, scientific machine learning, and Bayesian optimization for their ability to provide probabilistic predictions and model uncertainty. However, GP inference struggles to scale…

Machine Learning · Computer Science 2025-10-29 Pratik Rathore , Zachary Frangella , Sachin Garg , Shaghayegh Fazliani , Michał Dereziński , Madeleine Udell

Scientific and engineering problems often require the use of artificial intelligence to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners, they have…

Machine Learning · Computer Science 2021-07-01 Liwei Wang , Suraj Yerramilli , Akshay Iyer , Daniel Apley , Ping Zhu , Wei Chen

We introduce a stochastic variational inference procedure for training scalable Gaussian process (GP) models whose per-iteration complexity is independent of both the number of training points, $n$, and the number basis functions used in…

Machine Learning · Statistics 2020-06-05 Trefor W. Evans , Prasanth B. Nair

We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank…

Machine Learning · Statistics 2017-03-01 Pan Xu , Jian Ma , Quanquan Gu

A simple and widely adopted approach to extend Gaussian processes (GPs) to multiple outputs is to model each output as a linear combination of a collection of shared, unobserved latent GPs. An issue with this approach is choosing the number…

Machine Learning · Statistics 2019-12-18 Pavel Berkovich , Eric Perim , Wessel Bruinsma

Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that…

Methodology · Statistics 2022-11-22 Rafael Cabral , David Bolin , Håvard Rue

Gaussian processes (GPs) serve as flexible surrogates for complex surfaces, but buckle under the cubic cost of matrix decompositions with big training data sizes. Geospatial and machine learning communities suggest pseudo-inputs, or…

Methodology · Statistics 2021-02-05 D. Austin Cole , Ryan Christianson , Robert B. Gramacy

Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot…

Robotics · Computer Science 2017-05-18 Jing Dong , Byron Boots , Frank Dellaert

While recent work on conjugate gradient methods and Lanczos decompositions have achieved scalable Gaussian process inference with highly accurate point predictions, in several implementations these iterative methods appear to struggle with…

Machine Learning · Computer Science 2022-01-03 Wesley J. Maddox , Sanyam Kapoor , Andrew Gordon Wilson

Estimating causal effects in quasi-experiments with spatio-temporal panel data often requires adjusting for unmeasured confounding that varies across space and time. Gaussian Processes (GPs) offer a flexible, nonparametric modeling approach…

Methodology · Statistics 2025-07-08 Sofia L. Vega , Rachel C. Nethery