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Related papers: Linearly constrained Gaussian processes

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This work considers estimation and forecasting in a multivariate, possibly high-dimensional count time series model constructed from a transformation of a latent Gaussian dynamic factor series. The estimation of the latent model parameters…

Methodology · Statistics 2025-04-07 Younghoon Kim , Marie-Christine Düker , Zachary F. Fisher , Vladas Pipiras

This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential,…

Machine Learning · Computer Science 2017-09-13 Maziar Raissi , George Em. Karniadakis

In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…

Methodology · Statistics 2020-11-09 A. Fradi , Y. Feunteun , C. Samir , M. Baklouti , F. Bachoc , J-M. Loubes

Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…

Machine Learning · Statistics 2016-10-05 Benjamin Fischer , Nico Gorbach , Stefan Bauer , Yatao Bian , Joachim M. Buhmann

The paper deals with the problem of output regulation of nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. We borrow from the adaptive internal model design technique recently proposed in [1]…

Systems and Control · Electrical Eng. & Systems 2022-06-27 Lorenzo Gentilini , Michelangelo Bin , Lorenzo Marconi

Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…

Machine Learning · Statistics 2020-10-23 Jakob Lindinger , David Reeb , Christoph Lippert , Barbara Rakitsch

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

This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…

Numerical Analysis · Mathematics 2020-07-20 Aretha L Teckentrup

Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…

Methodology · Statistics 2026-03-10 Adam Gorm Hoffmann , Claus Thorn Ekstrøm , Andreas Kryger Jensen

This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…

Machine Learning · Statistics 2026-03-24 MD Ruiz-Medina , AE Madrid , A Torres-Signes , JM Angulo

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…

Statistics Theory · Mathematics 2009-09-29 Aad van der Vaart , Harry van Zanten

We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…

Machine Learning · Statistics 2018-05-23 Steven Atkinson , Nicholas Zabaras

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…

In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from…

Computer Vision and Pattern Recognition · Computer Science 2019-07-04 Zenith Purisha , Carl Jidling , Niklas Wahlström , Simo Särkkä , Thomas B. Schön

Data-driven Model Predictive Control (MPC), where the system model is learned from data with machine learning, has recently gained increasing interests in the control community. Gaussian Processes (GP), as a type of statistical models, are…

Systems and Control · Computer Science 2019-10-03 Truong X. Nghiem

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

Machine Learning · Statistics 2020-02-26 Ivan Ustyuzhaninov , Ieva Kazlauskaite , Carl Henrik Ek , Neill D. F. Campbell

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

We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…

Machine Learning · Statistics 2018-07-23 Martin Tegner , Benjamin Bloem-Reddy , Stephen Roberts

Gaussian Processes face two primary challenges: constructing models for large datasets and selecting the optimal model. This master's thesis tackles these challenges in the low-dimensional case. We examine recent convergence results to…

Machine Learning · Statistics 2024-11-13 Marcel Neugebauer

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

Machine Learning · Statistics 2014-04-08 Maurizio Filippone , Mark Girolami