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Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the…

Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior.…

Machine Learning · Computer Science 2023-03-20 Matthias Bitzer , Mona Meister , Christoph Zimmer

A neural architecture with randomly initialized weights, in the infinite width limit, is equivalent to a Gaussian Random Field whose covariance function is the so-called Neural Network Gaussian Process kernel (NNGP). We prove that a…

Machine Learning · Computer Science 2024-04-29 Rustem Takhanov

We propose a principled way to define Gaussian process priors on various sets of unweighted graphs: directed or undirected, with or without loops. We endow each of these sets with a geometric structure, inducing the notions of closeness and…

Machine Learning · Statistics 2023-02-28 Viacheslav Borovitskiy , Mohammad Reza Karimi , Vignesh Ram Somnath , Andreas Krause

It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success in adopting a deep network for feature extraction followed by a GP…

Machine Learning · Computer Science 2021-10-26 Chi-Ken Lu , Patrick Shafto

Accurate simulations of atomistic systems from first principles are limited by computational cost. In high-throughput settings, machine learning can reduce these costs significantly by accurately interpolating between reference…

Chemical Physics · Physics 2022-11-28 Haoyan Huo , Matthias Rupp

Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…

Machine Learning · Computer Science 2020-10-28 Feng Yin , Lishuo Pan , Xinwei He , Tianshi Chen , Sergios Theodoridis , Zhi-Quan , Luo

Amidst the growing interest in nonparametric regression, we address a significant challenge in Gaussian processes(GP) applied to manifold-based predictors. Existing methods primarily focus on low dimensional constrained domains for heat…

Optimization and Control · Mathematics 2024-02-01 Ke Ye , Mu Niu , Pokman Cheung , Zhenwen Dai , Yuan Liu

We introduce a new class of nonstationary kernels, which we derive as covariance functions of a novel family of stochastic processes we refer to as string Gaussian processes (string GPs). We construct string GPs to allow for multiple types…

Machine Learning · Statistics 2015-06-09 Yves-Laurent Kom Samo , Stephen Roberts

Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick…

Machine Learning · Statistics 2011-08-15 Ferenc Huszár , Simon Lacoste-Julien

With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained…

Quantum Physics · Physics 2024-06-19 Jun Dai , Roman V. Krems

Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like…

Machine Learning · Computer Science 2024-03-12 Kaiwen Wu , Jonathan Wenger , Haydn Jones , Geoff Pleiss , Jacob R. Gardner

A device called a 'Gaussian Boson Sampler' has initially been proposed as a near-term demonstration of classically intractable quantum computation. As recently shown, it can also be used to decide whether two graphs are isomorphic. Based on…

Quantum Physics · Physics 2020-03-18 Maria Schuld , Kamil Brádler , Robert Israel , Daiqin Su , Brajesh Gupt

In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as…

Machine Learning · Statistics 2016-08-22 Yves-Laurent Kom Samo , Stephen Roberts

(Abridged) We have developed a numerical software library for collisionless N-body simulations named "Phantom-GRAPE" which highly accelerates force calculations among particles by use of a new SIMD instruction set extension to the x86…

Instrumentation and Methods for Astrophysics · Physics 2015-06-04 Ataru Tanikawa , Kohji Yoshikawa , Keigo Nitadori , Takashi Okamoto

Learning the inverse dynamics of robots directly from data, adopting a black-box approach, is interesting for several real-world scenarios where limited knowledge about the system is available. In this paper, we propose a black-box model…

Robotics · Computer Science 2024-09-09 Giulio Giacomuzzos , Ruggero Carli , Diego Romeres , Alberto Dalla Libera

In this paper we investigate a link between state- space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state- space models are transformed into continuous time form and…

Machine Learning · Statistics 2016-10-27 Alexander Grigorievskiy , Juha Karhunen

Gaussian Process (GP) models are widely utilized as surrogate models in scientific and engineering fields. However, standard GP models are limited to continuous variables due to the difficulties in establishing correlation structures for…

Machine Learning · Statistics 2025-03-05 Mingyu Pu , Songhao Wang , Haowei Wang , Szu Hui Ng

This study introduces an innovative Gaussian Process (GP) model utilizing an ensemble kernel that integrates Radial Basis Function (RBF), Rational Quadratic, and Mat\'ern kernels for product sales forecasting. By applying Bayesian…

Machine Learning · Computer Science 2024-06-12 Shahin Mirshekari , Negin Hayeri Motedayen , Mohammad Ensaf

Capsule Networks attempt to represent patterns in images in a way that preserves hierarchical spatial relationships. Additionally, research has demonstrated that these techniques may be robust against adversarial perturbations. We present…

Machine Learning · Statistics 2019-06-10 Taylor Killian , Justin Goodwin , Olivia Brown , Sung-Hyun Son