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Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and…

Machine Learning · Statistics 2016-11-18 Andreas Svensson , Johan Dahlin , Thomas B. Schön

Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…

Optimization and Control · Mathematics 2025-05-01 Adrian Lepp , Jörn Tebbe , Andreas Besginow

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

Data Analysis, Statistics and Probability · Physics 2008-02-03 Radford M. Neal

Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…

Machine Learning · Computer Science 2022-02-24 Krista Longi , Jakob Lindinger , Olaf Duennbier , Melih Kandemir , Arto Klami , Barbara Rakitsch

Despite significant recent advances in probabilistic meta-learning, it is common for practitioners to avoid using deep learning models due to a comparative lack of interpretability. Instead, many practitioners simply use non-meta-models…

Machine Learning · Statistics 2025-04-25 Tommy Rochussen , Vincent Fortuin

We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…

Machine Learning · Statistics 2011-10-25 Cedric Archambeau , Francis Bach

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

Machine Learning · Statistics 2015-11-25 Leo L. Duan , Xia Wang , Rhonda D. Szczesniak

Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…

Machine Learning · Computer Science 2023-09-20 Elizabeth J Cross , Timothy J Rogers , Daniel J Pitchforth , Samuel J Gibson , Matthew R Jones

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…

Quantum Physics · Physics 2019-05-29 Zhikuan Zhao , Jack K. Fitzsimons , Joseph F. Fitzsimons

We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…

Machine Learning · Statistics 2019-02-20 Steven Atkinson , Nicholas Zabaras

This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori…

Methodology · Statistics 2011-06-17 Terrance Savitsky , Marina Vannucci , Naijun Sha

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

Statistics Theory · Mathematics 2015-03-06 Debdeep Pati , Anirban Bhattacharya , Guang Cheng

In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…

Statistics Theory · Mathematics 2017-11-01 Zuofeng Shang , Guang Cheng

Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…

Machine Learning · Statistics 2020-11-17 Metod Jazbec , Michael Pearce , Vincent Fortuin

Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…

Machine Learning · Computer Science 2020-04-10 Andrew Pensoneault , Xiu Yang , Xueyu Zhu

Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…

Machine Learning · Computer Science 2016-09-22 P. K. Srijith , P. Balamurugan , Shirish Shevade

Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the…

Optimization and Control · Mathematics 2024-02-07 Mickael Binois , Victor Picheny

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…

Machine Learning · Statistics 2018-05-30 Christian Donner , Manfred Opper

When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well…

Machine Learning · Computer Science 2021-04-20 Sarem Seitz

Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…

Machine Learning · Computer Science 2017-08-22 Sourish Das , Sasanka Roy , Rajiv Sambasivan