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Uncertainty quantification (UQ) has increasing importance in building robust high-performance and generalizable materials property prediction models. It can also be used in active learning to train better models by focusing on getting new…

Materials Science · Physics 2022-11-14 Daniel Varivoda , Rongzhi Dong , Sadman Sadeed Omee , Jianjun Hu

Gaussian processes offer an attractive framework for predictive modeling from longitudinal data, i.e., irregularly sampled, sparse observations from a set of individuals over time. However, such methods have two key shortcomings: (i) They…

Machine Learning · Statistics 2020-12-09 Junjie Liang , Yanting Wu , Dongkuan Xu , Vasant Honavar

Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…

Machine Learning · Computer Science 2022-06-22 Sattar Vakili , Jonathan Scarlett , Da-shan Shiu , Alberto Bernacchia

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

Machine-learning algorithms have gained popularity in recent years in the field of ecological modeling due to their promising results in predictive performance of classification problems. While the application of such algorithms has been…

Machine Learning · Statistics 2019-10-07 Patrick Schratz , Jannes Muenchow , Eugenia Iturritxa , Jakob Richter , Alexander Brenning

In this work we present a face alignment pipeline based on two novel methods: weighted splitting for K-cluster Regression Forests and 3D Affine Pose Regression for face shape initialization. Our face alignment method is based on the Local…

Computer Vision and Pattern Recognition · Computer Science 2017-06-07 Marek Kowalski , Jacek Naruniec

For many survey-based spatial modelling problems, responses are observed as spatially aggregated over survey regions due to limited resources. Covariates, from weather models and satellite imageries, can be observed at many different…

Applications · Statistics 2022-04-04 Harrison Zhu , Adam Howes , Owen van Eer , Maxime Rischard , Yingzhen Li , Dino Sejdinovic , Seth Flaxman

Gaussian process regression (GPR) model has been widely used to fit data when the regression function is unknown and its nice properties have been well established. In this article, we introduce an extended t-process regression (eTPR)…

Methodology · Statistics 2017-05-16 Z. Wang , J. Q. Shi , Y. Lee

Expensive ultrasonic anemometers are usually required to measure wind speed accurately. The aim of this work is to overcome the loss of accuracy of a low cost hot-wire anemometer caused by the changes of air temperature, by means of a…

Random forest regression is a powerful non-parametric method that adapts to local data characteristics through data-driven partitioning, making it effective across diverse application domains. However, the piecewise constant nature of…

Machine Learning · Computer Science 2026-05-19 Ziyi Liu , Phuc Luong , Mario Boley , Daniel F. Schmidt

A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize…

Machine Learning · Statistics 2022-04-13 Jonas Wacker , Maurizio Filippone

Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often a few parameters are sufficient to parameterize the covariance…

Machine Learning · Statistics 2021-01-01 Florian Gerber , Douglas W. Nychka

We present a probabilistic framework to accurately estimate dimensions of additively manufactured components. Using a dataset of 405 parts from nine production runs involving two machines, three polymer materials, and two-part…

Machine Learning · Computer Science 2025-09-23 Dipayan Sanpui , Anirban Chandra , Henry Chan , Sukriti Manna , Subramanian KRS Sankaranarayanan

The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…

Machine Learning · Computer Science 2021-08-02 Armin Lederer , Alejandro Jose Ordonez Conejo , Korbinian Maier , Wenxin Xiao , Jonas Umlauft , Sandra Hirche

Fourier feature approximations have been successfully applied in the literature for scalable Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived from Gaussian quadrature rules have gained popularity in…

Machine Learning · Statistics 2023-10-24 Kevin Li , Max Balakirsky , Simon Mak

We demonstrate how the Gaussian process regression approach can be used to efficiently reconstruct free energy surfaces from umbrella sampling simulations. By making a prior assumption of smoothness and taking account of the sampling noise…

Statistical Mechanics · Physics 2014-07-25 Thomas Stecher , Noam Bernstein , Gábor Csányi

The accurate predictions and principled uncertainty measures provided by GP regression incur O(n^3) cost which is prohibitive for modern-day large-scale applications. This has motivated extensive work on computationally efficient…

Machine Learning · Statistics 2023-12-29 Robert Allison , Anthony Stephenson , Samuel F , Edward Pyzer-Knapp

We propose methods for density estimation and data synthesis using a novel form of unsupervised random forests. Inspired by generative adversarial networks, we implement a recursive procedure in which trees gradually learn structural…

Machine Learning · Statistics 2023-03-14 David S. Watson , Kristin Blesch , Jan Kapar , Marvin N. Wright

Remote sensing observations are extensively used for analysis of environmental variables. These variables often exhibit spatial correlation, which has to be accounted for in the calibration models used in predictions, either by direct…

Applications · Statistics 2017-02-14 Virpi Junttila , Marko Laine

Real-time state estimation and forecasting is critical for efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for probabilistic forecasting and estimating…

Machine Learning · Statistics 2020-10-12 Tong Ma , David Alonso Barajas-Solano , Ramakrishna Tipireddy , Alexandre M. Tartakovsky