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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…

Machine Learning · Statistics 2025-08-26 Yuta Shikuri

In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The…

Numerical Analysis · Mathematics 2024-05-15 Phillip Semler , Martin Weiser

Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of…

Computation · Statistics 2018-12-20 Thomas Wutzler

In this paper we consider the problem of Gaussian process classifier (GPC) model selection with different Leave-One-Out (LOO) Cross Validation (CV) based optimization criteria and provide a practical algorithm using LOO predictive…

Machine Learning · Computer Science 2012-06-27 Sundararajan Sellamanickam , Sathiya Keerthi Selvaraj

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…

We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…

Optimization and Control · Mathematics 2022-04-18 Julien Pelamatti , Rodolphe Le Riche , Céline Helbert , Christophette Blanchet-Scalliet

Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and…

Machine Learning · Computer Science 2026-03-12 Hanlin Yu , Marcelo Hartmann , Bernardo Williams , Mark Girolami , Arto Klami

Latent Gaussian process (GP) models are flexible probabilistic non-parametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is…

Methodology · Statistics 2024-12-09 Pascal Kündig , Fabio Sigrist

Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when the number of observations is large, especially…

This paper compares three approaches to the problem of selecting among probability models to fit data (1) use of statistical criteria such as Akaike's information criterion and Schwarz's "Bayesian information criterion," (2) maximization of…

Methodology · Statistics 2016-11-04 William B. Poland , Ross D. Shachter

Posterior inference for Dirichlet process mixture models is analytically intractable and typically relies on Markov chain Monte Carlo methods, which can become computationally prohibitive at moderate to large sample sizes. In this work, we…

Computation · Statistics 2026-04-29 Beatrice Franzolini , Francesco Pozza

Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point…

Machine Learning · Statistics 2017-05-17 Hildo Bijl , Thomas B. Schön , Jan-Willem van Wingerden , Michel Verhaegen

Gaussian Process (GP) regression is shown to be effective for learning unknown dynamics, enabling efficient and safety-aware control strategies across diverse applications. However, existing GP-based model predictive control (GP-MPC)…

Systems and Control · Electrical Eng. & Systems 2025-05-13 Manish Prajapat , Johannes Köhler , Amon Lahr , Andreas Krause , Melanie N. Zeilinger

We propose a new method for simplification of Gaussian process (GP) models by projecting the information contained in the full encompassing model and selecting a reduced number of variables based on their predictive relevance. Our results…

Methodology · Statistics 2017-12-18 Juho Piironen , Aki Vehtari

The meta learning few-shot classification is an emerging problem in machine learning that received enormous attention recently, where the goal is to learn a model that can quickly adapt to a new task with only a few labeled data. We…

Machine Learning · Computer Science 2021-12-14 Minyoung Kim , Timothy Hospedales

Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…

Methodology · Statistics 2018-08-02 Yongxiang Li , Qiang Zhou , Kwok Leung Tsui , Javier Cabrera

State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and…

Approximate Bayesian computation (ABC) can be used for model fitting when the likelihood function is intractable but simulating from the model is feasible. However, even a single evaluation of a complex model may take several hours,…

Machine Learning · Statistics 2018-02-19 Marko Järvenpää , Michael Gutmann , Aki Vehtari , Pekka Marttinen

Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…

Machine Learning · Computer Science 2017-08-22 Sourish Das , Sasanka Roy , Rajiv Sambasivan

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…

Computation · Statistics 2011-08-03 Surya T Tokdar