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Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…

Numerical Analysis · Mathematics 2022-09-30 Andrei Chertkov , Gleb Ryzhakov , Georgii Novikov , Ivan Oseledets

This paper considers the Laplace method to derive approximate inference for the Gaussian process (GP) regression in the location and scale parameters of the Student-t probabilistic model. This allows both mean and variance of the data to…

Methodology · Statistics 2019-08-09 Marcelo Hartmann , Jarno Vanhatalo

The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the…

Computation · Statistics 2016-08-09 Aki Vehtari , Tommi Mononen , Ville Tolvanen , Tuomas Sivula , Ole Winther

Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…

Machine Learning · Computer Science 2025-06-27 Michalis K. Titsias

Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a…

Machine Learning · Statistics 2012-11-06 Krzysztof Chalupka , Christopher K. I. Williams , Iain Murray

Gaussian processes provide a powerful probabilistic kernel learning framework, which allows learning high quality nonparametric regression models via methods such as Gaussian process regression. Nevertheless, the learning phase of Gaussian…

Numerical Analysis · Mathematics 2021-01-06 Paz Fink Shustin , Haim Avron

Bayesian optimization with Gaussian process as surrogate model has been successfully applied to analog circuit synthesis. In the traditional Gaussian process regression model, the kernel functions are defined explicitly. The computational…

Machine Learning · Computer Science 2019-12-03 Shuhan Zhang , Wenlong Lyu , Fan Yang , Changhao Yan , Dian Zhou , Xuan Zeng

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models…

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the…

Machine Learning · Computer Science 2019-04-19 Ángel F. García-Fernández , Filip Tronarp , Simo Särkkä

Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…

Computation · Statistics 2020-11-09 Charles C. Margossian , Aki Vehtari , Daniel Simpson , Raj Agrawal

Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when the number of observations is large, especially…

Recognizing the successes of treed Gaussian process (TGP) models as an interpretable and thrifty model for nonparametric regression, we seek to extend the model to classification. Both treed models and Gaussian processes (GPs) have,…

Methodology · Statistics 2010-09-28 Tamara Broderick , Robert B. Gramacy

Deep learning has revolutionized the last decade, being at the forefront of extraordinary advances in a wide range of tasks including computer vision, natural language processing, and reinforcement learning, to name but a few. However, it…

Machine Learning · Computer Science 2024-01-24 Sebastian W. Ober

Modelling robot dynamics accurately is essential for control, motion optimisation and safe human-robot collaboration. Given the complexity of modern robotic systems, dynamics modelling remains non-trivial, mostly in the presence of…

Robotics · Computer Science 2022-05-11 David Jorge , Gabriella Pizzuto , Michael Mistry

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

Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…

Computation · Statistics 2025-07-31 Cristian A. Galvis-Florez , Ahmad Farooq , Simo Särkkä

Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets…

Machine Learning · Computer Science 2021-08-10 Clara Menzen , Manon Kok , Kim Batselier

Current methods for regularization in machine learning require quite specific model assumptions (e.g. a kernel shape) that are not derived from prior knowledge about the application, but must be imposed merely to make the method work. We…

Machine Learning · Statistics 2022-11-01 Matthias Wieler

Gaussian process (GP) models have been used in a wide range of battery applications, in which different kernels were manually selected with considerable expertise. However, to capture complex relationships in the ever-growing amount of…

Systems and Control · Electrical Eng. & Systems 2025-05-06 Huang Zhang , Xixi Liu , Faisal Altaf , Torsten Wik

It is common practice to use Laplace approximations to compute marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to…

Methodology · Statistics 2022-02-01 Jon Lachmann , Geir Storvik , Florian Frommlet , Aliaksadr Hubin