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We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the…
Covariance operators are fundamental in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen--Lo\`eve expansion. These operators may themselves be subject to variation, for…
Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…
In this paper we extend existing Bayesian methods for variable selection in Gaussian process regression, to select both the regression terms and the active covariates in the spatial correlation structure. We then use the estimated posterior…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…
Motivated by objects such as electric fields or fluid streams, we study the problem of learning stochastic fields, i.e. stochastic processes whose samples are fields like those occurring in physics and engineering. Considering general…
Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic…
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.…
Building spatial process models that capture nonstationary behavior while delivering computationally efficient inference is challenging. Nonstationary spatially varying kernels (see, e.g., Paciorek, 2003) offer flexibility and richness, but…
Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
This article explores the optimization of variational approximations for posterior covariances of Gaussian multiway arrays. To achieve this, we establish a natural differential geometric optimization framework on the space using the…
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…
Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…
We propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients. The method is based on a novel combination of the nonparametric kernel smoothing technique and a Lasso bias-corrected ridge…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
We consider Gaussian subordinated L\'evy fields (GSLFs) that arise by subordinating L\'evy processes with positive transformations of Gaussian random fields on some spatial domain $\mathcal{D}\subset \mathbb{R}^d$, $d\geq 1$. The resulting…
The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…