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Related papers: Convolutional Gaussian Processes

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We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…

Machine Learning · Computer Science 2019-05-15 Ian Walker , Ben Glocker

Previous work generally believes that improving the spatial invariance of convolutional networks is the key to object counting. However, after verifying several mainstream counting networks, we surprisingly found too strict pixel-level…

Computer Vision and Pattern Recognition · Computer Science 2022-08-19 Zhi-Qi Cheng , Qi Dai , Hong Li , JingKuan Song , Xiao Wu , Alexander G. Hauptmann

Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which…

Machine Learning · Statistics 2016-11-03 Andrew Gordon Wilson , Zhiting Hu , Ruslan Salakhutdinov , Eric P. Xing

The determination of the physical parameters of gravitational wave events is a fundamental pillar in the analysis of the signals observed by the current ground-based interferometers. Typically, this is done using Bayesian inference…

General Relativity and Quantum Cosmology · Physics 2023-11-07 M. Andrés-Carcasona , M. Martinez , Ll. M. Mir

The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…

Machine Learning · Statistics 2022-11-07 Vidhi Lalchand , Wessel P. Bruinsma , David R. Burt , Carl E. Rasmussen

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…

Machine Learning · Statistics 2018-08-17 Alexander G. de G. Matthews , Mark Rowland , Jiri Hron , Richard E. Turner , Zoubin Ghahramani

Gaussian processes offers a convenient way to perform nonparametric reconstructions of observational data assuming only a kernel which describes the covariance between neighbouring points in a data set. We approach the ambiguity in the…

Cosmology and Nongalactic Astrophysics · Physics 2021-08-17 Reginald Christian Bernardo , Jackson Levi Said

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…

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

Many applications in speech, robotics, finance, and biology deal with sequential data, where ordering matters and recurrent structures are common. However, this structure cannot be easily captured by standard kernel functions. To model such…

Machine Learning · Computer Science 2017-10-06 Maruan Al-Shedivat , Andrew Gordon Wilson , Yunus Saatchi , Zhiting Hu , Eric P. Xing

Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…

Machine Learning · Statistics 2011-03-22 Nicolas Durrande , David Ginsbourger , Olivier Roustant

In this paper, we present a comprehensive analysis of the posterior covariance field in Gaussian processes, with applications to the posterior covariance matrix. The analysis is based on the Gaussian prior covariance but the approach also…

Machine Learning · Statistics 2025-04-03 Difeng Cai , Edmond Chow , Yuanzhe Xi

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…

Numerical Analysis · Mathematics 2024-10-04 Daniel Sanz-Alonso , Ruiyi Yang

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Machine Learning · Statistics 2022-04-29 Alexander Terenin

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

Machine Learning · Statistics 2022-10-12 Marcus M. Noack , James A. Sethian

Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…

Machine Learning · Computer Science 2019-10-31 Gregory W. Benton , Wesley J. Maddox , Jayson P. Salkey , Julio Albinati , Andrew Gordon Wilson

We consider the optimal approximate posterior over the top-layer weights in a Bayesian neural network for regression, and show that it exhibits strong dependencies on the lower-layer weights. We adapt this result to develop a correlated…

Machine Learning · Statistics 2021-06-23 Sebastian W. Ober , Laurence Aitchison

Link prediction aims to reveal missing edges in a graph. We address this task with a Gaussian process that is transformed using simplified graph convolutions to better leverage the inductive bias of the domain. To scale the Gaussian process…

Machine Learning · Computer Science 2020-02-12 Felix L. Opolka , Pietro Liò

Interest in multioutput kernel methods is increasing, whether under the guise of multitask learning, multisensor networks or structured output data. From the Gaussian process perspective a multioutput Mercer kernel is a covariance function…

Machine Learning · Statistics 2009-12-18 Mauricio A. Álvarez , David Luengo , Michalis K. Titsias , Neil D. Lawrence

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…

Machine Learning · Statistics 2014-01-03 Andrew Gordon Wilson , Ryan Prescott Adams