Related papers: Multi-fidelity classification using Gaussian proce…

Class imbalance is a common problem in the case of real-world object detection and classification tasks. Data of some classes is abundant making them an over-represented majority, and data of other classes is scarce, making them an…

Sparse functional data frequently arise in real-world applications, posing significant challenges for accurate classification. To address this, we propose a novel classification method that integrates functional principal component analysis…

Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious…

Solving inverse problems in cardiovascular modeling is particularly challenging due to the high computational cost of running high-fidelity simulations. In this work, we focus on Bayesian parameter estimation and explore different methods…

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches…

High-fidelity physics simulations are powerful tools in the design and optimization of charged particle accelerators. However, the computational burden of these simulations often limits their use in practice for design optimization and…

Learning functions with high-dimensional outputs is critical in many applications, such as physical simulation and engineering design. However, collecting training examples for these applications is often costly, e.g. by running numerical…

Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the…

Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is…

We propose a new fiducial Markov Chain Monte Carlo (MCMC) method for fitting parametric Gaussian models. We utilize the Cayley transform to decompose the parametric covariance matrix, which in turn allows us to formulate a general data…

A central topic in functional data analysis is how to design an optimaldecision rule, based on training samples, to classify a data function. We exploit the optimal classification problem when data functions are Gaussian processes. Sharp…

We recapitulate the Bayesian formulation of neural network based classifiers and show that, while sampling from the posterior does indeed lead to better generalisation than is obtained by standard optimisation of the cost function, even…

Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…

Variational inference has recently emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) in large-scale Bayesian inference. The core idea is to trade statistical accuracy for computational efficiency. In this…

High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands…

Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…

Recommender systems are often designed based on a collaborative filtering approach, where user preferences are predicted by modelling interactions between users and items. Many common approaches to solve the collaborative filtering task are…

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…