Related papers: Combining additivity and active subspaces for high…
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…
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 classification is a popular method with a number of appealing properties. We show how to scale the model within a variational inducing point framework, outperforming the state of the art on benchmark datasets. Importantly,…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
For many survey-based spatial modelling problems, responses are observed as spatially aggregated over survey regions due to limited resources. Covariates, from weather models and satellite imageries, can be observed at many different…
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,…
We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in stochastic processes using lower dimensional projections. Our model combines the techniques…
Generalized additive model is a powerful statistical learning and predictive modeling tool that has been applied in a wide range of applications. The need of high-dimensional additive modeling is eminent in the context of dealing with high…
The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing…
In biomanufacturing, developing an accurate model to simulate the complex dynamics of bioprocesses is an important yet challenging task. This is partially due to the uncertainty associated with bioprocesses, high data acquisition cost, and…
In engineering design, one often wishes to calculate the probability that the performance of a system is satisfactory under uncertainty. State of the art algorithms exist to solve this problem using active learning with Gaussian process…
Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to…
Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…
In order to better model high-dimensional sequential data, we propose a collaborative multi-output Gaussian process dynamical system (CGPDS), which is a novel variant of GPDSs. The proposed model assumes that the output on each dimension is…
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…
The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process (GP) regression, a…
Bayesian optimization (BO) is a leading method for optimizing expensive black-box optimization and has been successfully applied across various scenarios. However, BO suffers from the curse of dimensionality, making it challenging to scale…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads…
With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…