Related papers: Bayesian inference for high-dimensional nonstation…
A central question in multimodal neuroimaging analysis is to understand the association between two imaging modalities and to identify brain regions where such an association is statistically significant. In this article, we propose a…
Gaussian processes (GPs) are powerful tools for nonlinear classification in which latent GPs are combined with link functions. But GPs do not scale well to large training data. This is compounded for classification where the latent GPs…
This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over…
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters…
Gaussian processes (GP) are a popular and powerful tool for spatial modelling of data, especially data that quantify environmental processes. However, in stationary form, whether covariance is isotropic or anisotropic, GPs may lack the…
Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…
We propose multivariate nonstationary Gaussian processes for jointly modeling multiple clinical variables, where the key parameters, length-scales, standard deviations and the correlations between the observed output, are all time…
Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
Deep Gaussian processes (DGPs) provide a rich class of models that can better represent functions with varying regimes or sharp changes, compared to conventional GPs. In this work, we propose a novel inference method for DGPs for computer…
Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the…
Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample…
This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…
Weakly stationary Gaussian processes (GPs) are the principal tool in the statistical approaches to the design and analysis of computer experiments (or Uncertainty Quantification). Such processes are fitted to computer model output using a…
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…
Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
Recent advances in the field of meta-learning have tackled domains consisting of large numbers of small ("few-shot") supervised learning tasks. Meta-learning algorithms must be able to rapidly adapt to any individual few-shot task, fitting…