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The Hubble parameter, $H(z)$, plays a crucial role in understanding the expansion history of the universe and constraining the Hubble constant, $\mathrm{H}_0$. The Cosmic Chronometers (CC) method provides an independent approach to…
By using recent $H(z)$ and SNe Ia data, we reconstruct the evolution of kinematic parameters $H(z)$, $q(z)$, jerk and snap, using a model-independent, non-parametric method, namely, the Gaussian Processes. Throughout the present analysis,…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
Direct observations of the Hubble rate, from cosmic chronometers and the radial baryon acoustic oscillation scale, can out-perform supernovae observations in understanding the expansion history, because supernovae observations need to be…
A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…
Prior beliefs about the latent function to shape inductive biases can be incorporated into a Gaussian Process (GP) via the kernel. However, beyond kernel choices, the decision-making process of GP models remains poorly understood. In this…
The Hilbert-space Gaussian Process (HGP) approach offers a hyperparameter-independent basis function approximation for speeding up Gaussian Process (GP) inference by projecting the GP onto M basis functions. These properties result in a…
The existing degeneracy between different dark energy and modified gravity cosmologies at the background level may be broken by analysing quantities at the perturbative level. In this work, we apply a non-parametric smoothing (NPS) method…
Gaussian processes (GPs) are used to make medical and scientific decisions, including in cardiac care and monitoring of atmospheric carbon dioxide levels. Notably, the choice of GP kernel is often somewhat arbitrary. In particular,…
Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
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…
Approximate Bayesian computation (ABC) can be used for model fitting when the likelihood function is intractable but simulating from the model is feasible. However, even a single evaluation of a complex model may take several hours,…
This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on…
The last two decades have seen a major expansion in the availability, size, and precision of time-domain datasets in astronomy. Owing to their unique combination of flexibility, mathematical simplicity and comparative robustness, Gaussian…
Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…
Gaussian Processes (GPs) are flexible, nonparametric Bayesian models widely used for regression and classification because of their ability to capture complex data patterns and quantify predictive uncertainty. However, the O(n^3)…
Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve…
Kernel methods have revolutionized the fields of pattern recognition and machine learning. Their success, however, critically depends on the choice of kernel parameters. Using Gaussian process (GP) classification as a working example, this…
Gaussian process (GP) is a powerful modeling method with applications in machine learning for various engineering and non-engineering fields. Despite numerous benefits of modeling using GPs, the computational complexity associated with GPs…