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Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…

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…

Efficient Reinforcement Learning usually takes advantage of demonstration or good exploration strategy. By applying posterior sampling in model-free RL under the hypothesis of GP, we propose Gaussian Process Posterior Sampling Reinforcement…

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…

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…

Bayesian modelling of dynamic systems must achieve a compromise between providing a complete mechanistic specification of the process while retaining the flexibility to handle those situations in which data is sparse relative to model…

Physical systems can often be described via a continuous-time dynamical system. In practice, the true system is often unknown and has to be learned from measurement data. Since data is typically collected in discrete time, e.g. by sensors,…

This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a…

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…

Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…

The proliferation of capable and efficient machine learning (ML) models marks one of the strongest methodological shifts in signal processing (SP) in its nearly 100-year history. ML models support the development of SP systems that…

The problem of effective equations is reviewed and discussed. Starting from the classical Langevin equation, we show how it can be generalized to Hamiltonian systems with non-standard kinetic terms. A numerical method for inferring…

Ensuring safety and adapting to the user's behavior are of paramount importance in physical human-robot interaction. Thus, incorporating elastic actuators in the robot's mechanical design has become popular, since it offers intrinsic…

Reinforcement learning provides a framework for learning to control which actions to take towards completing a task through trial-and-error. In many applications observing interactions is costly, necessitating sample-efficient learning. In…

The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…

Gaussian processes (GPs) are powerful but computationally expensive machine learning models, requiring an estimate of the kernel covariance matrix for every prediction. In large and complex domains, such as graphs, sets, or images, the…

High-fidelity simulations and physical experiments are essential for engineering analysis and design, yet their high cost often makes two critical tasks--global sensitivity analysis (GSA) and optimization--prohibitively expensive. This…

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…

Synchrophasor data provide unprecedented opportunities for inferring power system dynamics, such as estimating voltage angles, frequencies, and accelerations along with power injection at all buses. Aligned to this goal, this work puts…