We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing point approximation that is well-tailored to the convolutional kernel. This allows us to gain the generalisation benefit of a convolutional kernel, together wit...

Gaussian processes (GPs) enable probabilistic kernel-machines with remarkable modeling efficacy and GPML toolbox facilitates a widespread use by practitioners and researchers. Many modern applications demand non-metric (dis)similarities. As a result, Mercer’s condition for positive semidefiniteness is violated. Through a simple text categorization example that involves a KL-divergence based ker...

Warped Gaussian processes (WGP) [1] model output observations in regression tasks as a parametric nonlinear transformation of a Gaussian process (GP). The use of this nonlinear transformation, which is included as part of the probabilistic model, was shown to enhance performance by providing a better prior model on several data sets. In order to learn its parameters, maximum likelihood was used...

Although Gaussian process inference is usually formulated for a single output, in many machine learning problems the objective is to infer multiple tasks jointly, possibly exploring the dependencies between them to improve results. Real world examples of this problem include ore mining where the objective is to infer the concentration of several chemical components to assess the ore quality. Si...

Definition 1.1. A Gaussian process {Xt }t∈T indexed by a set T is a family of (real-valued) random variables Xt , all defined on the same probability space, such that for any finite subset F ⊂ T the random vector XF := {Xt }t∈F has a (possibly degenerate) Gaussian distribution; if these finitedimensional distributions are all non-degenerate then the Gaussian process is said to be nondegenerate....

We generalise the Gaussian process (GP) framework for regression by learning a nonlinear transformation of the GP outputs. This allows for non-Gaussian processes and non-Gaussian noise. The learning algorithm chooses a nonlinear transformation such that transformed data is well-modelled by a GP. This can be seen as including a preprocessing transformation as an integral part of the probabilisti...

We propose a multiresolution Gaussian process to capture long-range, non-Markovian dependencies while allowing for abrupt changes. The multiresolution GP hierarchically couples a collection of smooth GPs, each defined over an element of a random nested partition. Long-range dependencies are captured by the top-level GP while the partition points define the abrupt changes. Due to the inherent co...

Recently, new models for regression and classiication have been introduced which may be interpreted as neural networks in the limit of innnitely many parameters. For a regression model, the average case generalization performance is studied using a combination of information theoretic ideas and statistical mechanics methods.

To scale Gaussian processes (GPs) to large data sets we introduce the robust Bayesian Committee Machine (rBCM), a practical and scalable product-of-experts model for large-scale distributed GP regression. Unlike state-of-theart sparse GP approximations, the rBCM is conceptually simple and does not rely on inducing or variational parameters. The key idea is to recursively distribute computations...

Gaussian processes are usually parameterised in terms of their covariance functions. However, this makes it difficult to deal with multiple outputs, because ensuring that the covariance matrix is positive definite is problematic. An alternative formulation is to treat Gaussian processes as white noise sources convolved with smoothing kernels, and to parameterise the kernel instead. Using this, ...