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The Hubble diagram constructed using HII galaxies (HIIGx) and Giant extragalactic HII regions (GEHR) as standard candles already extends beyond the current reach of Type Ia SNe. A sample of 156 HIIGx and GEHR sources has been used…
We present a novel computational approach for extracting weak signals, whose exact location and width may be unknown, from complex background distributions with an arbitrary functional form. We focus on datasets that can be naturally…
Much focus was on the possible slowing down of cosmic acceleration under the dark energy parametrization. In the present paper, we investigate this subject using the Gaussian processes (GP), without resorting to a particular template of…
Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
We study observational constraints on the cosmographic functions up to the fourth derivative of the scale factor with respect to cosmic time, i.e., the so-called snap function, using the non-parametric method of Gaussian Processes. As…
Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…
In this letter, we propose an improved cosmological model-independent method to measure cosmic curvature, combining the recent measurements of transverse and line-of-sight directions in the baryon acoustic oscillations (BAO) with cosmic…
The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an…
Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…
We propose a representation of Gaussian processes (GPs) based on powers of the integral operator defined by a kernel function, we call these stochastic processes integral Gaussian processes (IGPs). Sample paths from IGPs are functions…
Accurately representing the sound field with the high spatial resolution is critical for immersive and interactive sound field reproduction technology. To minimize experimental effort, data-driven methods have been proposed to estimate…
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…
Using a fully Bayesian approach, Gaussian Process regression is extended to include marginalisation over the kernel choice and kernel hyperparameters. In addition, Bayesian model comparison via the evidence enables direct kernel comparison.…
Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…
Advances in hyperspectral imaging modes including electron energy loss spectroscopy (EELS) in scanning transmission electron microscopy (STEM) bring forth the challenges of exploratory and subsequently physics-based analysis of…
Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…
The cosmic curvature density parameter has been constrained in the present work independent of any background cosmological model. The reconstruction is performed adopting the non-parametric Gaussian Processes (GP). The constraints on…
Estimating causal effects in quasi-experiments with spatio-temporal panel data often requires adjusting for unmeasured confounding that varies across space and time. Gaussian Processes (GPs) offer a flexible, nonparametric modeling approach…