English
Related papers

Related papers: Optimising Gaussian processes for reconstructing d…

200 papers

Machine learning of multi-dimensional potential energy surfaces, from purely ab initio datasets, has seen substantial progress in the past years. Gaussian processes, a popular regression method, have been very successful at producing…

Chemical Physics · Physics 2023-01-11 Fabio E. A. Albertani , Alex J. W. Thom

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

In this paper, we analyze Gaussian processes using statistical mechanics. Although the input is originally multidimensional, we simplify our model by considering the input as one-dimensional for statistical mechanical analysis. Furthermore,…

Statistical Mechanics · Physics 2025-05-05 Jun Tsuzurugi

Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…

Machine Learning · Statistics 2016-04-19 Alan D. Saul , James Hensman , Aki Vehtari , Neil D. Lawrence

We study random series priors for estimating a functional parameter (f\in L^2[0,1]). We show that with a series prior with random truncation, Gaussian coefficients, and inverse gamma multiplicative scaling, it is possible to achieve…

Statistics Theory · Mathematics 2017-06-15 Jan van Waaij , Harry van Zanten

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

The optimization of atomic structures plays a pivotal role in understanding and designing materials with desired properties. However, conventional computational methods often struggle with the formidable task of navigating the vast…

Materials Science · Physics 2024-11-19 Peder Lyngby , Casper Larsen , Karsten Wedel Jacobsen

Gaussian processes are used in many machine learning applications that rely on uncertainty quantification. Recently, computational tools for working with these models in geometric settings, such as when inputs lie on a Riemannian manifold,…

Machine Learning · Statistics 2023-10-31 Paul Rosa , Viacheslav Borovitskiy , Alexander Terenin , Judith Rousseau

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

Machine Learning · Statistics 2019-09-12 Christian Agrell

Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious…

Machine Learning · Computer Science 2020-01-17 Raju Ram , Sabine Müller , Franz-Josef Pfreundt , Nicolas R. Gauger , Janis Keuper

We introduce constrained Gaussian process (CGP), a Gaussian process model for random functions that allows easy placement of mathematical constrains (e.g., non-negativity, monotonicity, etc) on its sample functions. CGP comes with…

Statistics Theory · Mathematics 2019-04-23 Jeremiah Zhe Liu

Reinforcement learning provides a framework for learning to control which actions to take towards completing a task through trial-and-error. In many applications observing interactions is costly, necessitating sample-efficient learning. In…

Machine Learning · Statistics 2020-11-04 Charles Gadd , Markus Heinonen , Harri Lähdesmäki , Samuel Kaski

Numerical simulation of complex optical structures enables their optimization with respect to specific objectives. Often, optimization is done by multiple successive parameter scans, which are time consuming and computationally expensive.…

Computational Physics · Physics 2017-07-27 P. -I. Schneider , X. Garcia Santiago , C. Rockstuhl , S. Burger

We present a Bayesian reconstruction algorithm that infers the three-dimensional large-scale matter distribution from the weak gravitational lensing effects measured in the image shapes of galaxies. The algorithm is designed to also work…

Cosmology and Nongalactic Astrophysics · Physics 2017-12-20 Vanessa Böhm , Stefan Hilbert , Maksim Greiner , Torsten A. Enßlin

Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…

Computation · Statistics 2024-02-02 Ahmad Farooq , Cristian A. Galvis-Florez , Simo Särkkä

The accuracy of Bayesian inference can be negatively affected by the use of inaccurate forward models. In the case of gravitational-wave inference, accurate but computationally expensive waveform models are sometimes substituted with faster…

Instrumentation and Methods for Astrophysics · Physics 2024-04-02 Miaoxin Liu , Xiao-Dong Li , Alvin J. K. Chua

The main aim of this paper is to perform a model comparison for some reconstructions of the key properties that describe the dark energy of the Universe i.e. energy density and the equation of state (EoS). We carry out this process by using…

Cosmology and Nongalactic Astrophysics · Physics 2023-03-28 Luis A. Escamilla , J. Alberto Vazquez

We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…

Machine Learning · Statistics 2017-07-20 Tomoharu Iwata , Zoubin Ghahramani

Let us consider the deconvolution problem, that is, to recover a latent source $x(\cdot)$ from the observations $\mathbf{y} = [y_1,\ldots,y_N]$ of a convolution process $y = x\star h + \eta$, where $\eta$ is an additive noise, the…

Machine Learning · Statistics 2023-07-19 Felipe Tobar , Arnaud Robert , Jorge F. Silva

Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…

Machine Learning · Computer Science 2022-12-21 Felix Leibfried , Vincent Dutordoir , ST John , Nicolas Durrande