Related papers: Scalable Gaussian Processes: Advances in Iterative…
Large-scale precision matrix estimation is of fundamental importance yet challenging in many contemporary applications for recovering Gaussian graphical models. In this paper, we suggest a new approach of innovated scalable efficient…
Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…
This thesis focuses on Bayesian optimization with the improvements coming from two aspects:(i) the use of derivative information to accelerate the optimization convergence; and (ii) the consideration of scalable GPs for handling massive…
Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about…
Sequential algorithms are popular for experimental design, enabling emulation, optimisation and inference to be efficiently performed. For most of these applications bespoke software has been developed, but the approach is general and many…
Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…
Gaussian process classification (GPC) provides a flexible and powerful statistical framework describing joint distributions over function space. Conventional GPCs however suffer from (i) poor scalability for big data due to the full kernel…
We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…
Gaussian processes with derivative information are useful in many settings where derivative information is available, including numerous Bayesian optimization and regression tasks that arise in the natural sciences. Incorporating derivative…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…
Gaussian Processes face two primary challenges: constructing models for large datasets and selecting the optimal model. This master's thesis tackles these challenges in the low-dimensional case. We examine recent convergence results to…
One obstacle to the use of Gaussian processes (GPs) in large-scale problems, and as a component in deep learning system, is the need for bespoke derivations and implementations for small variations in the model or inference. In order to…
We present a kernel-independent method that applies hierarchical matrices to the problem of maximum likelihood estimation for Gaussian processes. The proposed approximation provides natural and scalable stochastic estimators for its…
Monitoring daily weather fields is critical for climate science, agriculture, and environmental planning, yet fully probabilistic spatio-temporal models become computationally prohibitive at continental scale. We present a case study on…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…
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…
Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with…