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Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…
Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for…
Multi-fidelity approaches combine different models built on a scarce but accurate data-set (high-fidelity data-set), and a large but approximate one (low-fidelity data-set) in order to improve the prediction accuracy. Gaussian Processes…
Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the…
Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are probabilistic and non-parametric…
In this paper, we propose \texttt{FGPR}: a Federated Gaussian process ($\mathcal{GP}$) regression framework that uses an averaging strategy for model aggregation and stochastic gradient descent for local client computations. Notably, the…
In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models,…
Gaussian processes (GP) are powerful tools for probabilistic modeling purposes. They can be used to define prior distributions over latent functions in hierarchical Bayesian models. The prior over functions is defined implicitly by the mean…
Established techniques for simulation and prediction with Gaussian process (GP) dynamics often implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error…
The periodic Gaussian process (PGP) has been increasingly used to model periodic data due to its high accuracy. Yet, computing the likelihood of PGP has a high computational complexity of $\mathcal{O}\left(n^{3}\right)$ ($n$ is the data…
A novel extrapolation method is proposed for longitudinal forecasting. A hierarchical Gaussian process model is used to combine nonlinear population change and individual memory of the past to make prediction. The prediction error is…
Long-term forecasting involves predicting a horizon that is far ahead of the last observation. It is a problem of high practical relevance, for instance for companies in order to decide upon expensive long-term investments. Despite the…
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…
Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…
Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
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 processes (GPs) are powerful non-parametric function estimators. However, their applications are largely limited by the expensive computational cost of the inference procedures. Existing stochastic or distributed synchronous…
Inter-domain Gaussian processes (GPs) allow for high flexibility and low computational cost when performing approximate inference in GP models. They are particularly suitable for modeling data exhibiting global structure but are limited to…
Grid-based modelling is widely used for estimating stellar parameters. However, stellar model grid is sparse because of the computational cost. This paper demonstrates an application of a machine-learning algorithm using the Gaussian…