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Surrogate models are often used to replace costly-to-evaluate complex coastal codes to achieve substantial computational savings. In many of those models, the hydrometeorological forcing conditions (inputs) or flood events (outputs) are…
We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…
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…
This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…
We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However,…
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…
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…
Design of experiments is a fundamental topic in applied statistics with a long history. Yet its application is often limited by the complexity and costliness of constructing experimental designs, which involve searching a high-dimensional…
The Gaussian process state space model (GPSSM) is a non-linear dynamical system, where unknown transition and/or measurement mappings are described by GPs. Most research in GPSSMs has focussed on the state estimation problem, i.e.,…
Multi-output regression seeks to borrow strength and leverage commonalities across different but related outputs in order to enhance learning and prediction accuracy. A fundamental assumption is that the output/group membership labels for…
Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of…
Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
Computational models providing accurate estimates of their uncertainty are crucial for risk management associated with decision making in healthcare contexts. This is especially true since many state-of-the-art systems are trained using the…
We study in this paper two classes of experimental designs, support points and projected support points, which can provide robust and effective emulation of computer experiments with Gaussian processes. These designs have two important…
Bilevel optimization problems can be used to represent the collaborative interaction between a power system and grid-connected entities, called the followers, such as data centers. Most existing approaches assume that such followers'…
In this paper we address a classification problem where two sources of labels with different levels of fidelity are available. Our approach is to combine data from both sources by applying a co-kriging schema on latent functions, which…
We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…
Computer experiments have become ubiquitous in science and engineering. Commonly, runs of these simulations demand considerable time and computing, making experimental design extremely important in gaining high quality information with…
We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally…