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Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…
Gaussian processes (GPs) are sophisticated distributions to model functional data. Whilst theoretically appealing, they are computationally cumbersome except for small datasets. We implement two methods for scaling GP inference in Stan:…
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…
Gaussian processes are flexible probabilistic regression models which are widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, full-scale approximations…
Conventional variational autoencoders fail in modeling correlations between data points due to their use of factorized priors. Amortized Gaussian process inference through GP-VAEs has led to significant improvements in this regard, but is…
Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…
Gaussian processes (GPs) are typically criticised for their unfavourable scaling in both computational and memory requirements. For large datasets, sparse GPs reduce these demands by conditioning on a small set of inducing variables…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
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…
Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…
We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…
A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
Gaussian Processes (\textbf{GPs}) are flexible non-parametric models with strong probabilistic interpretation. While being a standard choice for performing inference on time series, GPs have few techniques to work in a streaming setting.…
Gaussian process (GP) emulators have become essential tools for approximating complex simulators, significantly reducing computational demands in optimization, sensitivity analysis, and model calibration. While traditional GP emulators…
The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…
While Gaussian processes (GPs) are the method of choice for regression tasks, they also come with practical difficulties, as inference cost scales cubic in time and quadratic in memory. In this paper, we introduce a natural and expressive…
Generalized additive models (GAMs) are a widely used class of models of interest to statisticians as they provide a flexible way to design interpretable models of data beyond linear models. We here propose a scalable and well-calibrated…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
While recent work on conjugate gradient methods and Lanczos decompositions have achieved scalable Gaussian process inference with highly accurate point predictions, in several implementations these iterative methods appear to struggle with…