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Kernel ridge regression (KRR) and Gaussian processes (GPs) are fundamental tools in statistics and machine learning, with recent applications to highly over-parameterized deep neural networks. The ability of these tools to learn a target…

Gaussian processes (GPs) have been extensively utilized as nonparametric models for component separation in 21 cm data analyses. This exploits the distinct spectral behavior of the cosmological and foreground signals, which are modeled…

Learning the unknown causal parameters of a linear structural causal model is a fundamental task in causal analysis. The task, known as the problem of identification, asks to estimate the parameters of the model from a combination of…

Modeling epidemic spread is critical for informing policy decisions aimed at mitigation. Accordingly, in this work we present a new data-driven method based on Gaussian process regression (GPR) to model epidemic spread through the…

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

The extraction of parton distribution functions (PDFs) from experimental or lattice QCD data is an ill-posed inverse problem, where regularization strongly impacts both systematic uncertainties and the reliability of the results. We study a…

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…

Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…

Kernel ridge regression (KRR) is widely used for nonparametric regression over reproducing kernel Hilbert spaces. It offers powerful modeling capabilities at the cost of significant computational costs, which typically require $O(n^3)$…

In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…

Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs…

The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and…

Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random…

We introduce the convolutional spectral kernel (CSK), a novel family of non-stationary, nonparametric covariance kernels for Gaussian process (GP) models, derived from the convolution between two imaginary radial basis functions. We present…

Gaussian Radial Basis Function (RBF) Kernels are the most-often-employed kernels in artificial intelligence and machine learning routines for providing optimally-best results in contrast to their respective counter-parts. However, a little…

This work presents a novel method for extracting potential barrier distributions from experimental fusion cross sections. We utilize a simple Gaussian process regression (GPR) framework to model the observed cross sections as a function of…

Multi-output regression models must exploit dependencies between outputs to maximise predictive performance. The application of Gaussian processes (GPs) to this setting typically yields models that are computationally demanding and have…

We revisit widely used preferential Gaussian processes by Chu et al.(2005) and challenge their modelling assumption that imposes rankability of data items via latent utility function values. We propose a generalisation of pgp which can…

Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which…