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The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…

Methodology · Statistics 2014-02-14 Yue Wu , Jose Miguel Hernandez Lobato , Zoubin Ghahramani

Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that…

Machine Learning · Statistics 2018-11-13 Marton Havasi , José Miguel Hernández-Lobato , Juan José Murillo-Fuentes

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Machine Learning · Computer Science 2014-08-12 Jie Chen , Nannan Cao , Kian Hsiang Low , Ruofei Ouyang , Colin Keng-Yan Tan , Patrick Jaillet

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Machine Learning · Statistics 2013-05-27 Jie Chen , Nannan Cao , Kian Hsiang Low , Ruofei Ouyang , Colin Keng-Yan Tan , Patrick Jaillet

This work presents a macroscopic model for the flow of two immiscible and incompressible fluids within inhomogeneous porous media. At the pore scale, the flow is governed by the full Navier-Stokes equations while the phase interface…

Fluid Dynamics · Physics 2026-03-02 Chunhua Zhang , Peiyao Liu , Cheng Peng , Lian-Ping Wang , Zhaoli Guo

We derive a Matern Gaussian process (GP) on the vertices of a hypergraph. This enables estimation of regression models of observed or latent values associated with the vertices, in which the correlation and uncertainty estimates are…

Machine Learning · Statistics 2021-06-04 Thomas Pinder , Kathryn Turnbull , Christopher Nemeth , David Leslie

Gaussian process (GP) priors are non-parametric generative models with appealing modelling properties for Bayesian inference: they can model non-linear relationships through noisy observations, have closed-form expressions for training and…

Machine Learning · Statistics 2020-01-31 Gonzalo Rios

We present and discuss a novel approach to deal with conservation properties for the simulation of nonlinear complex porous media flows in the presence of: 1) multiscale heterogeneity structures appearing in the elliptic-pressure-velocity…

Numerical Analysis · Mathematics 2020-06-15 Juan Galvis , Eduardo Abreu , Ciro Diaz , Jonh Perez

Recent research has shown the potential utility of Deep Gaussian Processes. These deep structures are probability distributions, designed through hierarchical construction, which are conditionally Gaussian. In this paper, the current…

Statistics Theory · Mathematics 2018-08-20 Matthew M. Dunlop , Mark A. Girolami , Andrew M. Stuart , Aretha L. Teckentrup

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

Numerical Analysis · Mathematics 2025-04-24 Jonas Latz , Aretha L. Teckentrup , Simon Urbainczyk

Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems,…

Machine Learning · Statistics 2020-12-10 Juan Emmanuel Johnson , Valero Laparra , Gustau Camps-Valls

Deep Gaussian processes (DGPs) upgrade ordinary GPs through functional composition, in which intermediate GP layers warp the original inputs, providing flexibility to model non-stationary dynamics. Two DGP regimes have emerged in recent…

Computation · Statistics 2022-08-16 Annie Sauer , Andrew Cooper , Robert B. Gramacy

Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…

Methodology · Statistics 2021-10-19 Didong Li , Andrew Jones , Sudipto Banerjee , Barbara E. Engelhardt

In this work, we propose a non-parametric probabilistic load flow (NP-PLF) technique based on the Gaussian Process (GP) learning to understand the power system behavior under uncertainty for better operational decisions. The technique can…

Systems and Control · Electrical Eng. & Systems 2020-03-19 Parikshit Pareek , Chuan Wang , Hung D. Nguyen

Obtaining accurate water level predictions are essential for water resource management and implementing flood mitigation strategies. Several data-driven models can be found in the literature. However, there has been limited research with…

Applications · Statistics 2025-06-27 Victor Hugo Nagahama , James Sweeney , Niamh Cahill

Gaussian processes (GPs) are widely used as surrogate models for emulating computer code, which simulate complex physical phenomena. In many problems, additional boundary information (i.e., the behavior of the phenomena along input…

Methodology · Statistics 2019-08-26 Liang Ding , Simon Mak , C. F. Jeff Wu

The estimation of the permeability of porous media to fluids is of fundamental importance in fields as diverse as oil and gas industry, agriculture, hydrology and medicine. Despite more than 150 years since the publication of Darcy's linear…

Fluid Dynamics · Physics 2024-06-07 Tairone Paiva Leão

The multiphase flow mechanism in miscible displacement through porous media is an important topic in various applications, such as petroleum engineering, low Reynolds number suspension flows, dusty gas dynamics, and fluidized beds. To…

Fluid Dynamics · Physics 2017-05-03 M. Jalal Ahammad , Jahrul M Alam

Modern scientific problems are often multi-disciplinary and require integration of computer models from different disciplines, each with distinct functional complexities, programming environments, and computation times. Linked Gaussian…

Machine Learning · Statistics 2023-06-05 Deyu Ming , Daniel Williamson

We present Flow-Induced Diagonal Gaussian Processes (FiD-GP), a compression framework that incorporates a compact inducing weight matrix to project a neural network's weight uncertainty into a lower-dimensional subspace. Critically, FiD-GP…

Machine Learning · Computer Science 2025-10-06 Moule Lin , Andrea Patane , Weipeng Jing , Shuhao Guan , Goetz Botterweck