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Aggregate data often appear in various fields such as socio-economics and public security. The aggregate data are associated not with points but with supports (e.g., spatial regions in a city). Since the supports may have various…

Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…

Machine Learning · Statistics 2021-11-22 Fergus Simpson , Vidhi Lalchand , Carl Edward Rasmussen

Gaussian process (GP) models have received increasing attention in recent years due to their superb prediction accuracy and modeling flexibility. To address the computational burdens of GP models for large-scale datasets, distributed…

Machine Learning · Statistics 2026-02-11 Haoyuan Chen , Rui Tuo

Fitness functions based on test cases are very common in Genetic Programming (GP). This process can be assimilated to a learning task, with the inference of models from a limited number of samples. This paper is an investigation on two…

Machine Learning · Computer Science 2016-08-16 Christian Gagné , Marc Schoenauer , Marc Parizeau , Marco Tomassini

A single-index model (SIM) provides for parsimonious multi-dimensional nonlinear regression by combining parametric (linear) projection with univariate nonparametric (non-linear) regression models. We show that a particular Gaussian process…

Methodology · Statistics 2011-08-18 Robert B. Gramacy , Heng Lian

LLMs are sensitive to prompting, with task performance often hinging on subtle, sometimes imperceptible variations in phrasing. As a result, crafting effective prompts manually remains challenging and time-consuming. Recent automatic…

Computation and Language · Computer Science 2025-12-01 Pawel Batorski , Paul Swoboda

Gaussian process (GP) regression is a Bayesian nonparametric method for regression and interpolation, offering a principled way of quantifying the uncertainties of predicted function values. For the quantified uncertainties to be…

Statistics Theory · Mathematics 2025-08-22 Masha Naslidnyk , Motonobu Kanagawa , Toni Karvonen , Maren Mahsereci

Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables…

Machine Learning · Statistics 2019-05-15 Hugh Salimbeni , Vincent Dutordoir , James Hensman , Marc Peter Deisenroth

Multi-output Gaussian Processes provide principled uncertainty-aware learning of vector-valued fields but are difficult to deploy in large-scale, distributed, and streaming settings due to their computational and centralized nature. This…

Machine Learning · Computer Science 2026-04-14 Yogesh Prasanna Kumar Rao , Tamas Keviczky , Raj Thilak Rajan

In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

Methodology · Statistics 2020-10-02 Hossein Mohammadi , Peter Challenor , Marc Goodfellow , Daniel Williamson

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

This document serves to complement our website which was developed with the aim of exposing the students to Gaussian Processes (GPs). GPs are non-parametric Bayesian regression models that are largely used by statisticians and geospatial…

Machine Learning · Computer Science 2018-09-07 Kshitij Tiwari

The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…

Methodology · Statistics 2024-04-02 Lulu Kang , Yuanxing Cheng , Yiwei Wang , Chun Liu

The stochastic partial differential equation approach to Gaussian processes (GPs) represents Mat\'ern GP priors in terms of $n$ finite element basis functions and Gaussian coefficients with sparse precision matrix. Such representations…

Computation · Statistics 2022-04-11 Daniel Sanz-Alonso , Ruiyi Yang

Learning uncertain dynamics models using Gaussian process~(GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability,…

Optimization and Control · Mathematics 2024-09-17 Manish Prajapat , Amon Lahr , Johannes Köhler , Andreas Krause , Melanie N. Zeilinger

Many datasets are in the form of tables of binned data. Performing regression on these data usually involves either reading off bin heights, ignoring data from neighbouring bins or interpolating between bins thus over or underestimating the…

Machine Learning · Statistics 2019-05-21 Michael Thomas Smith , Mauricio A Alvarez , Neil D Lawrence

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

Computer simulations often involve both qualitative and numerical inputs. Existing Gaussian process (GP) methods for handling this mainly assume a different response surface for each combination of levels of the qualitative factors and…

Machine Learning · Statistics 2019-01-31 Yichi Zhang , Siyu Tao , Wei Chen , Daniel W. Apley

Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical…

Probability · Mathematics 2016-06-07 Hassan Maatouk , Xavier Bay

This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…

Methodology · Statistics 2019-06-27 Casey B. Davis , Christopher M. Hans , Thomas J. Santner