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Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…

Quantum Physics · Physics 2019-05-20 Zhikuan Zhao , Alejandro Pozas-Kerstjens , Patrick Rebentrost , Peter Wittek

Gaussian process training decomposes into inference of the (approximate) posterior and learning of the hyperparameters. For non-Gaussian (non-conjugate) likelihoods, two common choices for approximate inference are Expectation Propagation…

Machine Learning · Computer Science 2022-11-14 Rui Li , ST John , Arno Solin

The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. It is theoretically compelling since it can be seen as a Gaussian process posterior with the mean function…

Machine Learning · Computer Science 2023-07-13 Agustinus Kristiadi , Alexander Immer , Runa Eschenhagen , Vincent Fortuin

Model selection aims to find the best model in terms of accuracy, interpretability or simplicity, preferably all at once. In this work, we focus on evaluating model performance of Gaussian process models, i.e. finding a metric that provides…

Machine Learning · Computer Science 2024-03-15 Andreas Besginow , Jan David Hüwel , Thomas Pawellek , Christian Beecks , Markus Lange-Hegermann

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

Machine Learning · Computer Science 2010-02-23 Yuan Qi , Ahmed H. Abdel-Gawad , Thomas P. Minka

Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach…

Machine Learning · Statistics 2020-04-07 Vidhi Lalchand , Carl Edward Rasmussen

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…

Numerical Analysis · Mathematics 2026-02-10 Daniel Hayes , Jing-Mei Qiu , Tianyi Shi

The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…

Statistics Theory · Mathematics 2025-06-17 Mikołaj J. Kasprzak , Ryan Giordano , Tamara Broderick

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

Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that…

Machine Learning · Computer Science 2024-07-02 Brent Sprangers , Nick Vannieuwenhoven

Forecasting in probabilistic time series is a complex endeavor that extends beyond predicting future values to also quantifying the uncertainty inherent in these predictions. Gaussian process regression stands out as a Bayesian machine…

Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…

Systems and Control · Electrical Eng. & Systems 2025-10-14 Muzaffar Qureshi , Tochukwu Elijah Ogri , Zachary I. Bell , Wanjiku A. Makumi , Rushikesh Kamalapurkar

We develop variational Laplace for Bayesian neural networks (BNNs) which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The…

Machine Learning · Statistics 2021-07-21 Ali Unlu , Laurence Aitchison

We develop variational Laplace for Bayesian neural networks (BNNs) which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The…

Machine Learning · Statistics 2021-08-11 Ali Unlu , Laurence Aitchison

Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…

Machine Learning · Computer Science 2023-06-27 Zhen Qin , Alexander Lidiak , Zhexuan Gong , Gongguo Tang , Michael B. Wakin , Zhihui Zhu

Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…

Machine Learning · Computer Science 2020-08-25 Vladimir Joukov , Dana Kulić

Deep neural networks (DNN) and Gaussian processes (GP) are two powerful models with several theoretical connections relating them, but the relationship between their training methods is not well understood. In this paper, we show that…

Machine Learning · Statistics 2020-07-21 Mohammad Emtiyaz Khan , Alexander Immer , Ehsan Abedi , Maciej Korzepa

This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest…

Machine Learning · Computer Science 2019-12-06 Tong Teng , Jie Chen , Yehong Zhang , Kian Hsiang Low

Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable. To address this issue, existing methods use a fully factorized structure (or a mixture of such…

Machine Learning · Computer Science 2020-05-19 Shibo Li , Wei Xing , Mike Kirby , Shandian Zhe

Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large…

Machine Learning · Computer Science 2014-10-01 Beyza Ermis , A. Taylan Cemgil