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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…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
Gaussian Process Regression (GPR) is widely used in statistics and machine learning for prediction tasks requiring uncertainty measures. Its efficacy depends on the appropriate specification of the mean function, covariance kernel function,…
Gaussian process priors are a popular choice for Bayesian analysis of regression problems. However, the implementation of these models can be complex, and ensuring that the implementation is correct can be challenging. In this paper we…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Bayesian inference and Gaussian processes are widely used in applications ranging from robotics and control to biological systems. Many of these applications are safety-critical and require a characterization of the uncertainty associated…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…
We address uncertainty quantification for Gaussian processes (GPs) under misspecified priors, with an eye towards Bayesian Optimization (BO). GPs are widely used in BO because they easily enable exploration based on posterior uncertainty…
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
Gaussian processes (GPs) are a mature and widely-used component of the ML toolbox. One of their desirable qualities is automatic hyperparameter selection, which allows for training without user intervention. However, in many realistic…
We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly…
It is common to model a deterministic response function, such as the output of a computer experiment, as a Gaussian process with a Mat\'ern covariance kernel. The smoothness parameter of a Mat\'ern kernel determines many important…
Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models,…
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…
We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…
Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…