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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 probabilistic and non-parametric…
Gaussian Process (GP) models are a powerful and flexible tool for non-parametric regression and classification. Computation for GP models is intensive, since computing the posterior density, $\pi$, for covariance function parameters…
The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…
We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…
We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…
In this paper, we investigate a class of approximate Gaussian processes (GP) obtained by taking a linear combination of compactly supported basis functions with the basis coefficients endowed with a dependent Gaussian prior distribution.…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…
Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…
Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…
Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…
A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…
Estimation of patient-specific model parameters is important for personalized modeling, although sparse and noisy clinical data can introduce significant uncertainty in the estimated parameter values. This importance source of uncertainty,…
Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the…
Gaussian process (GP) models that combine both categorical and continuous input variables have found use in analysis of longitudinal data and computer experiments. However, standard inference for these models has the typical cubic scaling,…
Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true…
Gaussian Processes (GPs) are widely used tools in statistics, machine learning, robotics, computer vision, and scientific computation. However, despite their popularity, they can be difficult to apply; all but the simplest classification or…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
We introduce a Fourier-based fast algorithm for Gaussian process regression in low dimensions. It approximates a translationally-invariant covariance kernel by complex exponentials on an equispaced Cartesian frequency grid of $M$ nodes.…